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shinaoka/meanfieldising.ipynb

Last active December 27, 2023 02:39
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Solving a self-consistent mean-field equation for Ising model
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meanfieldising.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Solving a self-consistent mean-field equation for Ising model"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using Plots\n",
"using Roots\n",
"using LaTeXStrings"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\tanh(x) = \\frac{4k_\\mathrm{B}T}{Jz} x,\n",
"$$\n",
"where $J$ is the exchange coupling and $z$ is the coordination number.\n",
"Here, we take $k_\\mathrm{B}=1$ and $J=1$.\n",
"The critical temperature is given by $T_\\mathrm{c} = z/4$.\n",
"\n",
"For a square lattice, $z = 4$."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"z = 4\n",
"J = 1"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xs = collect(LinRange(-2, 2, 100))\n",
"\n",
"y1 = tanh.(xs)\n",
"\n",
"p = plot()\n",
"plot!(p, xs, y1, label=\"tanh(x)\", legend=:topleft)\n",
"plot!(p, xs, 1.5 .* xs, label=\"1.5 * x\", legend=:topleft)\n",
"plot!(p, xs, 1.0 .* xs, label=\"1.0 * x\", legend=:topleft)\n",
"plot!(p, xs, 0.7 .* xs, label=\"0.7 * x\", legend=:topleft)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"compute_xcross (generic function with 1 method)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"function compute_xcross(temperature)\n",
" f(x) = tanh(x) - temperature * x\n",
" if f(1e-10) * f(1000.0) > 0\n",
" return 0.0\n",
" end\n",
" find_zero(f, (1e-10, 1000.0))\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"temperatures = collect(LinRange(0.1, 1.1, 1500))\n",
"moments = [0.5 * t * compute_xcross(t) for t in temperatures]\n",
";"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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1233.29,186.115 1234.63,186.601 1235.97,187.087 1237.32,187.576 1238.66,188.066 1240,188.557 1241.34,189.051 1242.69,189.545 1244.03,190.041 1245.37,190.539 1246.71,191.038 1248.05,191.539 1249.4,192.041 1250.74,192.545 1252.08,193.051 1253.42,193.558 1254.77,194.066 1256.11,194.576 1257.45,195.088 1258.79,195.601 1260.14,196.116 1261.48,196.632 1262.82,197.15 1264.16,197.67 1265.5,198.191 1266.85,198.714 1268.19,199.238 1269.53,199.764 1270.87,200.292 1272.22,200.821 1273.56,201.351 1274.9,201.884 1276.24,202.417 1277.59,202.953 1278.93,203.49 1280.27,204.029 1281.61,204.569 1282.96,205.111 1284.3,205.655 1285.64,206.2 1286.98,206.747 1288.32,207.295 1289.67,207.845 1291.01,208.397 1292.35,208.951 1293.69,209.506 1295.04,210.062 1296.38,210.621 1297.72,211.18 1299.06,211.742 1300.41,212.305 1301.75,212.87 1303.09,213.437 1304.43,214.005 1305.77,214.575 1307.12,215.147 1308.46,215.72 1309.8,216.295 1311.14,216.872 1312.49,217.45 1313.83,218.03 1315.17,218.612 1316.51,219.195 1317.86,219.78 1319.2,220.367 1320.54,220.955 1321.88,221.546 1323.23,222.138 1324.57,222.731 1325.91,223.327 1327.25,223.924 1328.59,224.522 1329.94,225.123 1331.28,225.725 1332.62,226.329 1333.96,226.935 1335.31,227.542 1336.65,228.151 1337.99,228.762 1339.33,229.375 1340.68,229.989 1342.02,230.606 1343.36,231.224 1344.7,231.843 1346.04,232.465 1347.39,233.088 1348.73,233.713 1350.07,234.34 1351.41,234.968 1352.76,235.599 1354.1,236.231 1355.44,236.865 1356.78,237.5 1358.13,238.138 1359.47,238.777 1360.81,239.418 1362.15,240.061 1363.5,240.706 1364.84,241.353 1366.18,242.001 1367.52,242.651 1368.86,243.303 1370.21,243.957 1371.55,244.613 1372.89,245.27 1374.23,245.929 1375.58,246.591 1376.92,247.254 1378.26,247.918 1379.6,248.585 1380.95,249.254 1382.29,249.924 1383.63,250.596 1384.97,251.271 1386.32,251.947 1387.66,252.625 1389,253.304 1390.34,253.986 1391.68,254.67 1393.03,255.355 1394.37,256.043 1395.71,256.732 1397.05,257.423 1398.4,258.116 1399.74,258.811 1401.08,259.508 1402.42,260.207 1403.77,260.908 1405.11,261.61 1406.45,262.315 1407.79,263.021 1409.13,263.73 1410.48,264.44 1411.82,265.153 1413.16,265.867 1414.5,266.583 1415.85,267.302 1417.19,268.022 1418.53,268.744 1419.87,269.468 1421.22,270.194 1422.56,270.923 1423.9,271.653 1425.24,272.385 1426.59,273.119 1427.93,273.855 1429.27,274.593 1430.61,275.333 1431.95,276.075 1433.3,276.819 1434.64,277.566 1435.98,278.314 1437.32,279.064 1438.67,279.816 1440.01,280.571 1441.35,281.327 1442.69,282.085 1444.04,282.846 1445.38,283.608 1446.72,284.373 1448.06,285.14 1449.4,285.908 1450.75,286.679 1452.09,287.452 1453.43,288.227 1454.77,289.004 1456.12,289.783 1457.46,290.565 1458.8,291.348 1460.14,292.133 1461.49,292.921 1462.83,293.711 1464.17,294.503 1465.51,295.297 1466.86,296.093 1468.2,296.891 1469.54,297.691 1470.88,298.494 1472.22,299.299 1473.57,300.106 1474.91,300.915 1476.25,301.726 1477.59,302.539 1478.94,303.355 1480.28,304.173 1481.62,304.993 1482.96,305.815 1484.31,306.639 1485.65,307.466 1486.99,308.295 1488.33,309.126 1489.67,309.959 1491.02,310.794 1492.36,311.632 1493.7,312.472 1495.04,313.314 1496.39,314.159 1497.73,315.006 1499.07,315.855 1500.41,316.706 1501.76,317.559 1503.1,318.415 1504.44,319.273 1505.78,320.134 1507.13,320.997 1508.47,321.862 1509.81,322.729 1511.15,323.599 1512.49,324.471 1513.84,325.345 1515.18,326.222 1516.52,327.101 1517.86,327.982 1519.21,328.866 1520.55,329.752 1521.89,330.641 1523.23,331.531 1524.58,332.425 1525.92,333.32 1527.26,334.218 1528.6,335.119 1529.94,336.022 1531.29,336.927 1532.63,337.834 1533.97,338.745 1535.31,339.657 1536.66,340.572 1538,341.49 1539.34,342.409 1540.68,343.332 1542.03,344.257 1543.37,345.184 1544.71,346.114 1546.05,347.046 1547.4,347.981 1548.74,348.918 1550.08,349.858 1551.42,350.8 1552.76,351.745 1554.11,352.692 1555.45,353.642 1556.79,354.595 1558.13,355.55 1559.48,356.507 1560.82,357.467 1562.16,358.43 1563.5,359.395 1564.85,360.363 1566.19,361.334 1567.53,362.307 1568.87,363.283 1570.21,364.261 1571.56,365.242 1572.9,366.226 1574.24,367.212 1575.58,368.201 1576.93,369.192 1578.27,370.187 1579.61,371.184 1580.95,372.183 1582.3,373.186 1583.64,374.191 1584.98,375.198 1586.32,376.209 1587.67,377.222 1589.01,378.238 1590.35,379.257 1591.69,380.278 1593.03,381.302 1594.38,382.329 1595.72,383.359 1597.06,384.392 1598.4,385.427 1599.75,386.465 1601.09,387.506 1602.43,388.55 1603.77,389.597 1605.12,390.646 1606.46,391.699 1607.8,392.754 1609.14,393.812 1610.48,394.873 1611.83,395.937 1613.17,397.004 1614.51,398.073 1615.85,399.146 1617.2,400.222 1618.54,401.3 1619.88,402.382 1621.22,403.466 1622.57,404.553 1623.91,405.644 1625.25,406.737 1626.59,407.834 1627.94,408.933 1629.28,410.035 1630.62,411.141 1631.96,412.249 1633.3,413.361 1634.65,414.476 1635.99,415.593 1637.33,416.714 1638.67,417.838 1640.02,418.965 1641.36,420.095 1642.7,421.228 1644.04,422.365 1645.39,423.504 1646.73,424.647 1648.07,425.793 1649.41,426.942 1650.76,428.095 1652.1,429.25 1653.44,430.409 1654.78,431.571 1656.12,432.736 1657.47,433.905 1658.81,435.077 1660.15,436.252 1661.49,437.43 1662.84,438.612 1664.18,439.797 1665.52,440.985 1666.86,442.177 1668.21,443.372 1669.55,444.57 1670.89,445.772 1672.23,446.978 1673.57,448.186 1674.92,449.398 1676.26,450.614 1677.6,451.833 1678.94,453.056 1680.29,454.282 1681.63,455.511 1682.97,456.744 1684.31,457.981 1685.66,459.221 1687,460.464 1688.34,461.712 1689.68,462.962 1691.03,464.217 1692.37,465.475 1693.71,466.736 1695.05,468.002 1696.39,469.271 1697.74,470.543 1699.08,471.82 1700.42,473.1 1701.76,474.384 1703.11,475.671 1704.45,476.962 1705.79,478.258 1707.13,479.556 1708.48,480.859 1709.82,482.166 1711.16,483.476 1712.5,484.79 1713.84,486.108 1715.19,487.43 1716.53,488.756 1717.87,490.086 1719.21,491.42 1720.56,492.757 1721.9,494.099 1723.24,495.445 1724.58,496.795 1725.93,498.148 1727.27,499.506 1728.61,500.868 1729.95,502.234 1731.3,503.604 1732.64,504.979 1733.98,506.357 1735.32,507.74 1736.66,509.126 1738.01,510.517 1739.35,511.913 1740.69,513.312 1742.03,514.716 1743.38,516.124 1744.72,517.536 1746.06,518.953 1747.4,520.374 1748.75,521.8 1750.09,523.229 1751.43,524.664 1752.77,526.102 1754.11,527.546 1755.46,528.993 1756.8,530.446 1758.14,531.902 1759.48,533.364 1760.83,534.83 1762.17,536.3 1763.51,537.775 1764.85,539.255 1766.2,540.74 1767.54,542.229 1768.88,543.723 1770.22,545.222 1771.57,546.725 1772.91,548.234 1774.25,549.747 1775.59,551.265 1776.93,552.788 1778.28,554.316 1779.62,555.849 1780.96,557.386 1782.3,558.929 1783.65,560.477 1784.99,562.03 1786.33,563.588 1787.67,565.151 1789.02,566.719 1790.36,568.293 1791.7,569.871 1793.04,571.455 1794.38,573.045 1795.73,574.639 1797.07,576.239 1798.41,577.844 1799.75,579.455 1801.1,581.071 1802.44,582.692 1803.78,584.319 1805.12,585.952 1806.47,587.59 1807.81,589.233 1809.15,590.883 1810.49,592.538 1811.84,594.198 1813.18,595.865 1814.52,597.537 1815.86,599.215 1817.2,600.899 1818.55,602.589 1819.89,604.284 1821.23,605.986 1822.57,607.694 1823.92,609.408 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1317.86,219.78 1319.2,220.367 1320.54,220.955 1321.88,221.546 1323.23,222.138 1324.57,222.731 1325.91,223.327 1327.25,223.924 1328.59,224.522 1329.94,225.123 1331.28,225.725 1332.62,226.329 1333.96,226.935 1335.31,227.542 1336.65,228.151 1337.99,228.762 1339.33,229.375 1340.68,229.989 1342.02,230.606 1343.36,231.224 1344.7,231.843 1346.04,232.465 1347.39,233.088 1348.73,233.713 1350.07,234.34 1351.41,234.968 1352.76,235.599 1354.1,236.231 1355.44,236.865 1356.78,237.5 1358.13,238.138 1359.47,238.777 1360.81,239.418 1362.15,240.061 1363.5,240.706 1364.84,241.353 1366.18,242.001 1367.52,242.651 1368.86,243.303 1370.21,243.957 1371.55,244.613 1372.89,245.27 1374.23,245.929 1375.58,246.591 1376.92,247.254 1378.26,247.918 1379.6,248.585 1380.95,249.254 1382.29,249.924 1383.63,250.596 1384.97,251.271 1386.32,251.947 1387.66,252.625 1389,253.304 1390.34,253.986 1391.68,254.67 1393.03,255.355 1394.37,256.043 1395.71,256.732 1397.05,257.423 1398.4,258.116 1399.74,258.811 1401.08,259.508 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1571.56,365.242 1572.9,366.226 1574.24,367.212 1575.58,368.201 1576.93,369.192 1578.27,370.187 1579.61,371.184 1580.95,372.183 1582.3,373.186 1583.64,374.191 1584.98,375.198 1586.32,376.209 1587.67,377.222 1589.01,378.238 1590.35,379.257 1591.69,380.278 1593.03,381.302 1594.38,382.329 1595.72,383.359 1597.06,384.392 1598.4,385.427 1599.75,386.465 1601.09,387.506 1602.43,388.55 1603.77,389.597 1605.12,390.646 1606.46,391.699 1607.8,392.754 1609.14,393.812 1610.48,394.873 1611.83,395.937 1613.17,397.004 1614.51,398.073 1615.85,399.146 1617.2,400.222 1618.54,401.3 1619.88,402.382 1621.22,403.466 1622.57,404.553 1623.91,405.644 1625.25,406.737 1626.59,407.834 1627.94,408.933 1629.28,410.035 1630.62,411.141 1631.96,412.249 1633.3,413.361 1634.65,414.476 1635.99,415.593 1637.33,416.714 1638.67,417.838 1640.02,418.965 1641.36,420.095 1642.7,421.228 1644.04,422.365 1645.39,423.504 1646.73,424.647 1648.07,425.793 1649.41,426.942 1650.76,428.095 1652.1,429.25 1653.44,430.409 1654.78,431.571 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1740.69,513.312 1742.03,514.716 1743.38,516.124 1744.72,517.536 1746.06,518.953 1747.4,520.374 1748.75,521.8 1750.09,523.229 1751.43,524.664 1752.77,526.102 1754.11,527.546 1755.46,528.993 1756.8,530.446 1758.14,531.902 1759.48,533.364 1760.83,534.83 1762.17,536.3 1763.51,537.775 1764.85,539.255 1766.2,540.74 1767.54,542.229 1768.88,543.723 1770.22,545.222 1771.57,546.725 1772.91,548.234 1774.25,549.747 1775.59,551.265 1776.93,552.788 1778.28,554.316 1779.62,555.849 1780.96,557.386 1782.3,558.929 1783.65,560.477 1784.99,562.03 1786.33,563.588 1787.67,565.151 1789.02,566.719 1790.36,568.293 1791.7,569.871 1793.04,571.455 1794.38,573.045 1795.73,574.639 1797.07,576.239 1798.41,577.844 1799.75,579.455 1801.1,581.071 1802.44,582.692 1803.78,584.319 1805.12,585.952 1806.47,587.59 1807.81,589.233 1809.15,590.883 1810.49,592.538 1811.84,594.198 1813.18,595.865 1814.52,597.537 1815.86,599.215 1817.2,600.899 1818.55,602.589 1819.89,604.284 1821.23,605.986 1822.57,607.694 1823.92,609.408 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1909.83,733.992 1911.17,736.218 1912.51,738.454 1913.85,740.701 1915.19,742.959 1916.54,745.227 1917.88,747.506 1919.22,749.796 1920.56,752.097 1921.91,754.41 1923.25,756.734 1924.59,759.069 1925.93,761.416 1927.28,763.775 1928.62,766.146 1929.96,768.528 1931.3,770.923 1932.65,773.33 1933.99,775.75 1935.33,778.182 1936.67,780.627 1938.01,783.085 1939.36,785.556 1940.7,788.04 1942.04,790.537 1943.38,793.049 1944.73,795.573 1946.07,798.112 1947.41,800.665 1948.75,803.232 1950.1,805.814 1951.44,808.411 1952.78,811.022 1954.12,813.648 1955.47,816.29 1956.81,818.947 1958.15,821.62 1959.49,824.309 1960.83,827.014 1962.18,829.735 1963.52,832.473 1964.86,835.228 1966.2,838 1967.55,840.79 1968.89,843.597 1970.23,846.422 1971.57,849.266 1972.92,852.128 1974.26,855.009 1975.6,857.909 1976.94,860.829 1978.28,863.768 1979.63,866.728 1980.97,869.708 1982.31,872.709 1983.65,875.731 1985,878.775 1986.34,881.841 1987.68,884.929 1989.02,888.04 1990.37,891.174 1991.71,894.332 1993.05,897.515 1994.39,900.721 1995.74,903.953 1997.08,907.211 1998.42,910.495 1999.76,913.805 2001.1,917.143 2002.45,920.509 2003.79,923.903 2005.13,927.326 2006.47,930.78 2007.82,934.263 2009.16,937.778 2010.5,941.325 2011.84,944.904 2013.19,948.517 2014.53,952.165 2015.87,955.847 2017.21,959.566 2018.55,963.322 2019.9,967.116 2021.24,970.949 2022.58,974.823 2023.92,978.737 2025.27,982.695 2026.61,986.696 2027.95,990.743 2029.29,994.836 2030.64,998.978 2031.98,1003.17 2033.32,1007.41 2034.66,1011.71 2036.01,1016.06 2037.35,1020.47 2038.69,1024.93 2040.03,1029.46 2041.37,1034.05 2042.72,1038.71 2044.06,1043.44 2045.4,1048.23 2046.74,1053.11 2048.09,1058.06 2049.43,1063.09 2050.77,1068.21 2052.11,1073.42 2053.46,1078.73 2054.8,1084.13 2056.14,1089.64 2057.48,1095.26 2058.82,1101 2060.17,1106.86 2061.51,1112.86 2062.85,1119 2064.19,1125.29 2065.54,1131.75 2066.88,1138.38 2068.22,1145.2 2069.56,1152.24 2070.91,1159.5 2072.25,1167.01 2073.59,1174.8 2074.93,1182.89 2076.28,1191.34 2077.62,1200.19 2078.96,1209.49 2080.3,1219.33 2081.64,1229.8 2082.99,1241.05 2084.33,1253.28 2085.67,1266.78 2087.01,1282.08 2088.36,1300.13 2089.7,1323.35 2091.04,1365.88 2092.38,1384.24 2093.73,1384.24 2095.07,1384.24 2096.41,1384.24 2097.75,1384.24 2099.09,1384.24 2100.44,1384.24 2101.78,1384.24 2103.12,1384.24 2104.46,1384.24 2105.81,1384.24 2107.15,1384.24 2108.49,1384.24 2109.83,1384.24 2111.18,1384.24 2112.52,1384.24 2113.86,1384.24 2115.2,1384.24 2116.55,1384.24 2117.89,1384.24 2119.23,1384.24 2120.57,1384.24 2121.91,1384.24 2123.26,1384.24 2124.6,1384.24 2125.94,1384.24 2127.28,1384.24 2128.63,1384.24 2129.97,1384.24 2131.31,1384.24 2132.65,1384.24 2134,1384.24 2135.34,1384.24 2136.68,1384.24 2138.02,1384.24 2139.36,1384.24 2140.71,1384.24 2142.05,1384.24 2143.39,1384.24 2144.73,1384.24 2146.08,1384.24 2147.42,1384.24 2148.76,1384.24 2150.1,1384.24 2151.45,1384.24 2152.79,1384.24 2154.13,1384.24 2155.47,1384.24 2156.82,1384.24 2158.16,1384.24 2159.5,1384.24 2160.84,1384.24 2162.18,1384.24 2163.53,1384.24 2164.87,1384.24 2166.21,1384.24 2167.55,1384.24 2168.9,1384.24 2170.24,1384.24 2171.58,1384.24 2172.92,1384.24 2174.27,1384.24 2175.61,1384.24 2176.95,1384.24 2178.29,1384.24 2179.63,1384.24 2180.98,1384.24 2182.32,1384.24 2183.66,1384.24 2185,1384.24 2186.35,1384.24 2187.69,1384.24 2189.03,1384.24 2190.37,1384.24 2191.72,1384.24 2193.06,1384.24 2194.4,1384.24 2195.74,1384.24 2197.09,1384.24 2198.43,1384.24 2199.77,1384.24 2201.11,1384.24 2202.45,1384.24 2203.8,1384.24 2205.14,1384.24 2206.48,1384.24 2207.82,1384.24 2209.17,1384.24 2210.51,1384.24 2211.85,1384.24 2213.19,1384.24 2214.54,1384.24 2215.88,1384.24 2217.22,1384.24 2218.56,1384.24 2219.91,1384.24 2221.25,1384.24 2222.59,1384.24 2223.93,1384.24 2225.27,1384.24 2226.62,1384.24 2227.96,1384.24 2229.3,1384.24 2230.64,1384.24 2231.99,1384.24 2233.33,1384.24 2234.67,1384.24 2236.01,1384.24 2237.36,1384.24 2238.7,1384.24 2240.04,1384.24 2241.38,1384.24 2242.72,1384.24 2244.07,1384.24 2245.41,1384.24 2246.75,1384.24 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"</svg>\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(temperatures, moments, xlabel=L\"T\", ylabel=L\"m\", legend=:topleft, label=\"\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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1595.66,599.862 1596.99,601.432 1598.31,603.005 1599.63,604.581 1600.96,606.159 1602.28,607.74 1603.6,609.323 1604.93,610.909 1606.25,612.498 1607.58,614.09 1608.9,615.684 1610.22,617.281 1611.55,618.88 1612.87,620.483 1614.19,622.088 1615.52,623.695 1616.84,625.305 1618.17,626.918 1619.49,628.534 1620.81,630.152 1622.14,631.773 1623.46,633.397 1624.78,635.023 1626.11,636.652 1627.43,638.283 1628.75,639.918 1630.08,641.555 1631.4,643.194 1632.73,644.837 1634.05,646.482 1635.37,648.129 1636.7,649.78 1638.02,651.433 1639.34,653.088 1640.67,654.747 1641.99,656.408 1643.31,658.071 1644.64,659.738 1645.96,661.407 1647.29,663.079 1648.61,664.753 1649.93,666.43 1651.26,668.11 1652.58,669.793 1653.9,671.478 1655.23,673.166 1656.55,674.856 1657.87,676.55 1659.2,678.246 1660.52,679.944 1661.85,681.646 1663.17,683.35 1664.49,685.056 1665.82,686.766 1667.14,688.478 1668.46,690.192 1669.79,691.91 1671.11,693.63 1672.44,695.353 1673.76,697.078 1675.08,698.807 1676.41,700.537 1677.73,702.271 1679.05,704.007 1680.38,705.746 1681.7,707.488 1683.02,709.232 1684.35,710.979 1685.67,712.729 1687,714.481 1688.32,716.237 1689.64,717.994 1690.97,719.755 1692.29,721.518 1693.61,723.284 1694.94,725.053 1696.26,726.824 1697.58,728.598 1698.91,730.375 1700.23,732.154 1701.56,733.936 1702.88,735.721 1704.2,737.508 1705.53,739.299 1706.85,741.092 1708.17,742.887 1709.5,744.685 1710.82,746.486 1712.14,748.29 1713.47,750.097 1714.79,751.906 1716.12,753.717 1717.44,755.532 1718.76,757.349 1720.09,759.169 1721.41,760.992 1722.73,762.817 1724.06,764.645 1725.38,766.476 1726.71,768.309 1728.03,770.145 1729.35,771.984 1730.68,773.826 1732,775.67 1733.32,777.517 1734.65,779.367 1735.97,781.219 1737.29,783.074 1738.62,784.932 1739.94,786.792 1741.27,788.656 1742.59,790.521 1743.91,792.39 1745.24,794.261 1746.56,796.136 1747.88,798.012 1749.21,799.892 1750.53,801.774 1751.85,803.659 1753.18,805.546 1754.5,807.437 1755.83,809.33 1757.15,811.226 1758.47,813.124 1759.8,815.025 1761.12,816.929 1762.44,818.836 1763.77,820.745 1765.09,822.657 1766.41,824.572 1767.74,826.489 1769.06,828.41 1770.39,830.332 1771.71,832.258 1773.03,834.186 1774.36,836.117 1775.68,838.051 1777,839.988 1778.33,841.927 1779.65,843.869 1780.98,845.813 1782.3,847.761 1783.62,849.711 1784.95,851.664 1786.27,853.619 1787.59,855.578 1788.92,857.538 1790.24,859.502 1791.56,861.469 1792.89,863.438 1794.21,865.41 1795.54,867.384 1796.86,869.361 1798.18,871.341 1799.51,873.324 1800.83,875.31 1802.15,877.298 1803.48,879.289 1804.8,881.282 1806.12,883.279 1807.45,885.278 1808.77,887.28 1810.1,889.284 1811.42,891.292 1812.74,893.302 1814.07,895.314 1815.39,897.33 1816.71,899.348 1818.04,901.369 1819.36,903.392 1820.68,905.419 1822.01,907.448 1823.33,909.48 1824.66,911.514 1825.98,913.552 1827.3,915.592 1828.63,917.634 1829.95,919.68 1831.27,921.728 1832.6,923.779 1833.92,925.833 1835.25,927.889 1836.57,929.948 1837.89,932.01 1839.22,934.075 1840.54,936.142 1841.86,938.212 1843.19,940.285 1844.51,942.36 1845.83,944.438 1847.16,946.519 1848.48,948.603 1849.81,950.69 1851.13,952.779 1852.45,954.871 1853.78,956.965 1855.1,959.063 1856.42,961.163 1857.75,963.266 1859.07,965.371 1860.39,967.48 1861.72,969.591 1863.04,971.705 1864.37,973.821 1865.69,975.94 1867.01,978.062 1868.34,980.187 1869.66,982.315 1870.98,984.445 1872.31,986.578 1873.63,988.714 1874.95,990.852 1876.28,992.993 1877.6,995.137 1878.93,997.284 1880.25,999.433 1881.57,1001.59 1882.9,1003.74 1884.22,1005.9 1885.54,1008.06 1886.87,1010.22 1888.19,1012.39 1889.52,1014.56 1890.84,1016.73 1892.16,1018.9 1893.49,1021.08 1894.81,1023.26 1896.13,1025.44 1897.46,1027.63 1898.78,1029.81 1900.1,1032 1901.43,1034.2 1902.75,1036.39 1904.08,1038.59 1905.4,1040.79 1906.72,1043 1908.05,1045.2 1909.37,1047.41 1910.69,1049.63 1912.02,1051.84 1913.34,1054.06 1914.66,1056.28 1915.99,1058.5 1917.31,1060.73 1918.64,1062.96 1919.96,1065.19 1921.28,1067.43 1922.61,1069.66 1923.93,1071.9 1925.25,1074.15 1926.58,1076.39 1927.9,1078.64 1929.22,1080.89 1930.55,1083.14 1931.87,1085.4 1933.2,1087.66 1934.52,1089.92 1935.84,1092.19 1937.17,1094.45 1938.49,1096.72 1939.81,1099 1941.14,1101.27 1942.46,1103.55 1943.79,1105.83 1945.11,1108.12 1946.43,1110.4 1947.76,1112.69 1949.08,1114.98 1950.4,1117.28 1951.73,1119.58 1953.05,1121.88 1954.37,1124.18 1955.7,1126.49 1957.02,1128.8 1958.35,1131.11 1959.67,1133.42 1960.99,1135.74 1962.32,1138.06 1963.64,1140.38 1964.96,1142.71 1966.29,1145.03 1967.61,1147.37 1968.93,1149.7 1970.26,1152.03 1971.58,1154.37 1972.91,1156.72 1974.23,1159.06 1975.55,1161.41 1976.88,1163.76 1978.2,1166.11 1979.52,1168.47 1980.85,1170.82 1982.17,1173.19 1983.49,1175.55 1984.82,1177.92 1986.14,1180.29 1987.47,1182.66 1988.79,1185.03 1990.11,1187.41 1991.44,1189.79 1992.76,1192.17 1994.08,1194.56 1995.41,1196.95 1996.73,1199.34 1998.06,1201.73 1999.38,1204.13 2000.7,1206.53 2002.03,1208.93 2003.35,1211.34 2004.67,1213.75 2006,1216.16 2007.32,1218.57 2008.64,1220.99 2009.97,1223.41 2011.29,1225.83 2012.62,1228.25 2013.94,1230.68 2015.26,1233.11 2016.59,1235.54 2017.91,1237.98 2019.23,1240.42 2020.56,1242.86 2021.88,1245.3 2023.2,1247.75 2024.53,1250.2 2025.85,1252.65 2027.18,1255.11 2028.5,1257.56 2029.82,1260.02 2031.15,1262.49 2032.47,1264.95 2033.79,1267.42 2035.12,1269.89 2036.44,1272.37 2037.76,1274.84 2039.09,1277.32 2040.41,1279.81 2041.74,1282.29 2043.06,1284.78 2044.38,1287.27 2045.71,1289.77 2047.03,1292.26 2048.35,1294.76 2049.68,1297.26 2051,1299.77 2052.33,1302.28 2053.65,1304.79 2054.97,1307.3 2056.3,1309.81 2057.62,1312.33 2058.94,1314.85 2060.27,1317.38 2061.59,1319.91 2062.91,1322.44 2064.24,1324.97 2065.56,1327.5 2066.89,1330.04 2068.21,1332.58 2069.53,1335.13 2070.86,1337.67 2072.18,1340.22 2073.5,1342.77 2074.83,1345.33 2076.15,1347.88 2077.47,1350.44 2078.8,1353.01 2080.12,1355.57 2081.45,1358.14 2082.77,1360.71 2084.09,1363.29 2085.42,1365.86 2086.74,1368.44 2088.06,1371.03 2089.39,1373.61 2090.71,1376.2 2092.03,1378.79 2093.36,1381.38 2094.68,1383.98 2096.01,1384.24 2097.33,1384.24 2098.65,1384.24 2099.98,1384.24 2101.3,1384.24 2102.62,1384.24 2103.95,1384.24 2105.27,1384.24 2106.6,1384.24 2107.92,1384.24 2109.24,1384.24 2110.57,1384.24 2111.89,1384.24 2113.21,1384.24 2114.54,1384.24 2115.86,1384.24 2117.18,1384.24 2118.51,1384.24 2119.83,1384.24 2121.16,1384.24 2122.48,1384.24 2123.8,1384.24 2125.13,1384.24 2126.45,1384.24 2127.77,1384.24 2129.1,1384.24 2130.42,1384.24 2131.74,1384.24 2133.07,1384.24 2134.39,1384.24 2135.72,1384.24 2137.04,1384.24 2138.36,1384.24 2139.69,1384.24 2141.01,1384.24 2142.33,1384.24 2143.66,1384.24 2144.98,1384.24 2146.3,1384.24 2147.63,1384.24 2148.95,1384.24 2150.28,1384.24 2151.6,1384.24 2152.92,1384.24 2154.25,1384.24 2155.57,1384.24 2156.89,1384.24 2158.22,1384.24 2159.54,1384.24 2160.87,1384.24 2162.19,1384.24 2163.51,1384.24 2164.84,1384.24 2166.16,1384.24 2167.48,1384.24 2168.81,1384.24 2170.13,1384.24 2171.45,1384.24 2172.78,1384.24 2174.1,1384.24 2175.43,1384.24 2176.75,1384.24 2178.07,1384.24 2179.4,1384.24 2180.72,1384.24 2182.04,1384.24 2183.37,1384.24 2184.69,1384.24 2186.01,1384.24 2187.34,1384.24 2188.66,1384.24 2189.99,1384.24 2191.31,1384.24 2192.63,1384.24 2193.96,1384.24 2195.28,1384.24 2196.6,1384.24 2197.93,1384.24 2199.25,1384.24 2200.57,1384.24 2201.9,1384.24 2203.22,1384.24 2204.55,1384.24 2205.87,1384.24 2207.19,1384.24 2208.52,1384.24 2209.84,1384.24 2211.16,1384.24 2212.49,1384.24 2213.81,1384.24 2215.14,1384.24 2216.46,1384.24 2217.78,1384.24 2219.11,1384.24 2220.43,1384.24 2221.75,1384.24 2223.08,1384.24 2224.4,1384.24 2225.72,1384.24 2227.05,1384.24 2228.37,1384.24 2229.7,1384.24 2231.02,1384.24 2232.34,1384.24 2233.67,1384.24 2234.99,1384.24 2236.31,1384.24 2237.64,1384.24 2238.96,1384.24 2240.28,1384.24 2241.61,1384.24 2242.93,1384.24 2244.26,1384.24 2245.58,1384.24 2246.9,1384.24 2248.23,1384.24 2249.55,1384.24 2250.87,1384.24 2252.2,1384.24 2253.52,1384.24 2254.84,1384.24 2256.17,1384.24 2257.49,1384.24 2258.82,1384.24 2260.14,1384.24 2261.46,1384.24 2262.79,1384.24 2264.11,1384.24 2265.43,1384.24 2266.76,1384.24 2268.08,1384.24 2269.41,1384.24 2270.73,1384.24 2272.05,1384.24 2273.38,1384.24 2274.7,1384.24 2276.02,1384.24 2277.35,1384.24 2278.67,1384.24 2279.99,1384.24 2281.32,1384.24 2282.64,1384.24 2283.97,1384.24 2285.29,1384.24 2286.61,1384.24 2287.94,1384.24 2289.26,1384.24 2290.58,1384.24 2291.91,1384.24 2293.23,1384.24 \"/>\n",
"</svg>\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(temperatures, moments .^ 2, xlabel=L\"T\", ylabel=L\"m^2\", legend=:topleft, label=\"\")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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1749.57,1423.18 1756.59,1423.18 1763.6,1423.18 1770.61,1423.18 1777.63,1423.18 1784.64,1423.18 1791.65,1423.18 1798.67,1423.18 1805.68,1423.18 1812.7,1423.18 1819.71,1423.18 1826.72,1423.18 1833.74,1423.18 1840.75,1423.18 1847.76,1423.18 1854.78,1423.18 1861.79,1423.18 1868.81,1423.18 1875.82,1423.18 1882.83,1423.18 1889.85,1423.18 1896.86,1423.18 1903.87,1423.18 1910.89,1423.18 1917.9,1423.18 1924.92,1423.18 1931.93,1423.18 1938.94,1423.18 1945.96,1423.18 1952.97,1423.18 1959.98,1423.18 1967,1423.18 1974.01,1423.18 1981.03,1423.18 1988.04,1423.18 1995.05,1423.18 2002.07,1423.18 2009.08,1423.18 2016.1,1423.18 2023.11,1423.18 2030.12,1423.18 2037.14,1423.18 2044.15,1423.18 2051.16,1423.18 2058.18,1423.18 2065.19,1423.18 2072.21,1423.18 2079.22,1423.18 2086.23,1423.18 2093.25,1423.18 2100.26,1423.18 2107.27,1423.18 2114.29,1423.18 2121.3,1423.18 2128.32,1423.18 2135.33,1423.18 2142.34,1423.18 2149.36,1423.18 2156.37,1423.18 2163.38,1423.18 2170.4,1423.18 2177.41,1423.18 2184.43,1423.18 2191.44,1423.18 2198.45,1423.18 2205.47,1423.18 2212.48,1423.18 2219.49,1423.18 2226.51,1423.18 2233.52,1423.18 2240.54,1423.18 2247.55,1423.18 2254.56,1423.18 2261.58,1423.18 2268.59,1423.18 2275.6,1423.18 2282.62,1423.18 2289.63,1423.18 2296.65,1423.18 2303.66,1423.18 2310.67,1423.18 2317.69,1423.18 2324.7,1423.18 2331.71,1423.18 2338.73,1423.18 2345.74,1423.18 2352.76,1423.18 \"/>\n",
"</svg>\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(temperatures, moments .^ 2, xlabel=L\"T\", ylabel=L\"m^2\", legend=:topleft, label=\"\", xlims=(0.9, 1.1), ylims=(0.0, 0.1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Internal energy (内部エネルギー)\n",
"\n",
"$U = -\\frac{Nz Jm^2}{2}$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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810.115,1366.7 811.433,1366.5 812.752,1366.3 814.07,1366.1 815.389,1365.9 816.707,1365.7 818.026,1365.49 819.345,1365.29 820.663,1365.08 821.982,1364.87 823.3,1364.66 824.619,1364.44 825.937,1364.23 827.256,1364.01 828.574,1363.8 829.893,1363.58 831.211,1363.36 832.53,1363.14 833.848,1362.91 835.167,1362.69 836.485,1362.46 837.804,1362.23 839.123,1362 840.441,1361.77 841.76,1361.54 843.078,1361.3 844.397,1361.07 845.715,1360.83 847.034,1360.59 848.352,1360.35 849.671,1360.11 850.989,1359.86 852.308,1359.61 853.626,1359.37 854.945,1359.12 856.263,1358.87 857.582,1358.61 858.9,1358.36 860.219,1358.1 861.538,1357.85 862.856,1357.59 864.175,1357.32 865.493,1357.06 866.812,1356.8 868.13,1356.53 869.449,1356.26 870.767,1355.99 872.086,1355.72 873.404,1355.45 874.723,1355.17 876.041,1354.9 877.36,1354.62 878.678,1354.34 879.997,1354.06 881.315,1353.77 882.634,1353.49 883.953,1353.2 885.271,1352.91 886.59,1352.62 887.908,1352.33 889.227,1352.04 890.545,1351.74 891.864,1351.44 893.182,1351.14 894.501,1350.84 895.819,1350.54 897.138,1350.23 898.456,1349.93 899.775,1349.62 901.093,1349.31 902.412,1349 903.731,1348.68 905.049,1348.37 906.368,1348.05 907.686,1347.73 909.005,1347.41 910.323,1347.09 911.642,1346.76 912.96,1346.44 914.279,1346.11 915.597,1345.78 916.916,1345.45 918.234,1345.11 919.553,1344.78 920.871,1344.44 922.19,1344.1 923.508,1343.76 924.827,1343.41 926.146,1343.07 927.464,1342.72 928.783,1342.37 930.101,1342.02 931.42,1341.67 932.738,1341.31 934.057,1340.96 935.375,1340.6 936.694,1340.24 938.012,1339.88 939.331,1339.51 940.649,1339.15 941.968,1338.78 943.286,1338.41 944.605,1338.04 945.923,1337.66 947.242,1337.29 948.561,1336.91 949.879,1336.53 951.198,1336.15 952.516,1335.77 953.835,1335.38 955.153,1334.99 956.472,1334.6 957.79,1334.21 959.109,1333.82 960.427,1333.42 961.746,1333.03 963.064,1332.63 964.383,1332.23 965.701,1331.82 967.02,1331.42 968.338,1331.01 969.657,1330.6 970.976,1330.19 972.294,1329.78 973.613,1329.36 974.931,1328.95 976.25,1328.53 977.568,1328.11 978.887,1327.68 980.205,1327.26 981.524,1326.83 982.842,1326.4 984.161,1325.97 985.479,1325.54 986.798,1325.1 988.116,1324.67 989.435,1324.23 990.754,1323.79 992.072,1323.34 993.391,1322.9 994.709,1322.45 996.028,1322 997.346,1321.55 998.665,1321.09 999.983,1320.64 1001.3,1320.18 1002.62,1319.72 1003.94,1319.26 1005.26,1318.8 1006.58,1318.33 1007.89,1317.86 1009.21,1317.39 1010.53,1316.92 1011.85,1316.44 1013.17,1315.97 1014.49,1315.49 1015.81,1315.01 1017.12,1314.53 1018.44,1314.04 1019.76,1313.55 1021.08,1313.07 1022.4,1312.57 1023.72,1312.08 1025.04,1311.59 1026.35,1311.09 1027.67,1310.59 1028.99,1310.09 1030.31,1309.58 1031.63,1309.08 1032.95,1308.57 1034.27,1308.06 1035.58,1307.55 1036.9,1307.03 1038.22,1306.52 1039.54,1306 1040.86,1305.48 1042.18,1304.95 1043.49,1304.43 1044.81,1303.9 1046.13,1303.37 1047.45,1302.84 1048.77,1302.3 1050.09,1301.77 1051.41,1301.23 1052.72,1300.69 1054.04,1300.15 1055.36,1299.6 1056.68,1299.06 1058,1298.51 1059.32,1297.96 1060.64,1297.4 1061.95,1296.85 1063.27,1296.29 1064.59,1295.73 1065.91,1295.17 1067.23,1294.6 1068.55,1294.04 1069.87,1293.47 1071.18,1292.9 1072.5,1292.32 1073.82,1291.75 1075.14,1291.17 1076.46,1290.59 1077.78,1290.01 1079.1,1289.42 1080.41,1288.84 1081.73,1288.25 1083.05,1287.66 1084.37,1287.06 1085.69,1286.47 1087.01,1285.87 1088.32,1285.27 1089.64,1284.67 1090.96,1284.06 1092.28,1283.46 1093.6,1282.85 1094.92,1282.24 1096.24,1281.63 1097.55,1281.01 1098.87,1280.39 1100.19,1279.77 1101.51,1279.15 1102.83,1278.53 1104.15,1277.9 1105.47,1277.27 1106.78,1276.64 1108.1,1276 1109.42,1275.37 1110.74,1274.73 1112.06,1274.09 1113.38,1273.45 1114.7,1272.8 1116.01,1272.16 1117.33,1271.51 1118.65,1270.85 1119.97,1270.2 1121.29,1269.54 1122.61,1268.89 1123.93,1268.22 1125.24,1267.56 1126.56,1266.9 1127.88,1266.23 1129.2,1265.56 1130.52,1264.89 1131.84,1264.21 1133.15,1263.53 1134.47,1262.86 1135.79,1262.17 1137.11,1261.49 1138.43,1260.8 1139.75,1260.12 1141.07,1259.42 1142.38,1258.73 1143.7,1258.04 1145.02,1257.34 1146.34,1256.64 1147.66,1255.94 1148.98,1255.23 1150.3,1254.52 1151.61,1253.81 1152.93,1253.1 1154.25,1252.39 1155.57,1251.67 1156.89,1250.95 1158.21,1250.23 1159.53,1249.51 1160.84,1248.78 1162.16,1248.06 1163.48,1247.33 1164.8,1246.59 1166.12,1245.86 1167.44,1245.12 1168.76,1244.38 1170.07,1243.64 1171.39,1242.89 1172.71,1242.15 1174.03,1241.4 1175.35,1240.65 1176.67,1239.89 1177.98,1239.14 1179.3,1238.38 1180.62,1237.62 1181.94,1236.85 1183.26,1236.09 1184.58,1235.32 1185.9,1234.55 1187.21,1233.78 1188.53,1233 1189.85,1232.22 1191.17,1231.44 1192.49,1230.66 1193.81,1229.88 1195.13,1229.09 1196.44,1228.3 1197.76,1227.51 1199.08,1226.71 1200.4,1225.92 1201.72,1225.12 1203.04,1224.32 1204.36,1223.51 1205.67,1222.71 1206.99,1221.9 1208.31,1221.09 1209.63,1220.27 1210.95,1219.46 1212.27,1218.64 1213.59,1217.82 1214.9,1216.99 1216.22,1216.17 1217.54,1215.34 1218.86,1214.51 1220.18,1213.68 1221.5,1212.84 1222.81,1212.01 1224.13,1211.17 1225.45,1210.32 1226.77,1209.48 1228.09,1208.63 1229.41,1207.78 1230.73,1206.93 1232.04,1206.07 1233.36,1205.22 1234.68,1204.36 1236,1203.5 1237.32,1202.63 1238.64,1201.77 1239.96,1200.9 1241.27,1200.03 1242.59,1199.15 1243.91,1198.28 1245.23,1197.4 1246.55,1196.52 1247.87,1195.63 1249.19,1194.75 1250.5,1193.86 1251.82,1192.97 1253.14,1192.07 1254.46,1191.18 1255.78,1190.28 1257.1,1189.38 1258.42,1188.47 1259.73,1187.57 1261.05,1186.66 1262.37,1185.75 1263.69,1184.84 1265.01,1183.92 1266.33,1183 1267.64,1182.08 1268.96,1181.16 1270.28,1180.23 1271.6,1179.31 1272.92,1178.38 1274.24,1177.44 1275.56,1176.51 1276.87,1175.57 1278.19,1174.63 1279.51,1173.69 1280.83,1172.74 1282.15,1171.79 1283.47,1170.84 1284.79,1169.89 1286.1,1168.94 1287.42,1167.98 1288.74,1167.02 1290.06,1166.06 1291.38,1165.09 1292.7,1164.12 1294.02,1163.15 1295.33,1162.18 1296.65,1161.21 1297.97,1160.23 1299.29,1159.25 1300.61,1158.27 1301.93,1157.28 1303.25,1156.3 1304.56,1155.31 1305.88,1154.31 1307.2,1153.32 1308.52,1152.32 1309.84,1151.32 1311.16,1150.32 1312.47,1149.31 1313.79,1148.31 1315.11,1147.3 1316.43,1146.28 1317.75,1145.27 1319.07,1144.25 1320.39,1143.23 1321.7,1142.21 1323.02,1141.19 1324.34,1140.16 1325.66,1139.13 1326.98,1138.1 1328.3,1137.06 1329.62,1136.02 1330.93,1134.98 1332.25,1133.94 1333.57,1132.9 1334.89,1131.85 1336.21,1130.8 1337.53,1129.75 1338.85,1128.69 1340.16,1127.63 1341.48,1126.57 1342.8,1125.51 1344.12,1124.45 1345.44,1123.38 1346.76,1122.31 1348.08,1121.23 1349.39,1120.16 1350.71,1119.08 1352.03,1118 1353.35,1116.92 1354.67,1115.83 1355.99,1114.75 1357.3,1113.65 1358.62,1112.56 1359.94,1111.47 1361.26,1110.37 1362.58,1109.27 1363.9,1108.16 1365.22,1107.06 1366.53,1105.95 1367.85,1104.84 1369.17,1103.73 1370.49,1102.61 1371.81,1101.49 1373.13,1100.37 1374.45,1099.25 1375.76,1098.12 1377.08,1096.99 1378.4,1095.86 1379.72,1094.73 1381.04,1093.59 1382.36,1092.45 1383.68,1091.31 1384.99,1090.17 1386.31,1089.02 1387.63,1087.87 1388.95,1086.72 1390.27,1085.57 1391.59,1084.41 1392.91,1083.25 1394.22,1082.09 1395.54,1080.92 1396.86,1079.76 1398.18,1078.59 1399.5,1077.42 1400.82,1076.24 1402.14,1075.06 1403.45,1073.88 1404.77,1072.7 1406.09,1071.52 1407.41,1070.33 1408.73,1069.14 1410.05,1067.95 1411.36,1066.75 1412.68,1065.55 1414,1064.35 1415.32,1063.15 1416.64,1061.94 1417.96,1060.74 1419.28,1059.53 1420.59,1058.31 1421.91,1057.1 1423.23,1055.88 1424.55,1054.66 1425.87,1053.43 1427.19,1052.21 1428.51,1050.98 1429.82,1049.75 1431.14,1048.51 1432.46,1047.28 1433.78,1046.04 1435.1,1044.8 1436.42,1043.55 1437.74,1042.31 1439.05,1041.06 1440.37,1039.8 1441.69,1038.55 1443.01,1037.29 1444.33,1036.03 1445.65,1034.77 1446.97,1033.51 1448.28,1032.24 1449.6,1030.97 1450.92,1029.69 1452.24,1028.42 1453.56,1027.14 1454.88,1025.86 1456.19,1024.58 1457.51,1023.29 1458.83,1022 1460.15,1020.71 1461.47,1019.42 1462.79,1018.12 1464.11,1016.82 1465.42,1015.52 1466.74,1014.22 1468.06,1012.91 1469.38,1011.6 1470.7,1010.29 1472.02,1008.98 1473.34,1007.66 1474.65,1006.34 1475.97,1005.02 1477.29,1003.69 1478.61,1002.37 1479.93,1001.04 1481.25,999.703 1482.57,998.368 1483.88,997.03 1485.2,995.69 1486.52,994.347 1487.84,993.001 1489.16,991.653 1490.48,990.302 1491.8,988.948 1493.11,987.592 1494.43,986.233 1495.75,984.872 1497.07,983.508 1498.39,982.141 1499.71,980.772 1501.02,979.4 1502.34,978.025 1503.66,976.648 1504.98,975.268 1506.3,973.886 1507.62,972.501 1508.94,971.113 1510.25,969.723 1511.57,968.33 1512.89,966.935 1514.21,965.537 1515.53,964.136 1516.85,962.732 1518.17,961.326 1519.48,959.918 1520.8,958.506 1522.12,957.092 1523.44,955.676 1524.76,954.257 1526.08,952.835 1527.4,951.41 1528.71,949.983 1530.03,948.554 1531.35,947.121 1532.67,945.686 1533.99,944.249 1535.31,942.808 1536.63,941.365 1537.94,939.92 1539.26,938.472 1540.58,937.021 1541.9,935.567 1543.22,934.111 1544.54,932.652 1545.85,931.191 1547.17,929.727 1548.49,928.26 1549.81,926.791 1551.13,925.319 1552.45,923.844 1553.77,922.367 1555.08,920.887 1556.4,919.405 1557.72,917.919 1559.04,916.432 1560.36,914.941 1561.68,913.448 1563,911.952 1564.31,910.454 1565.63,908.952 1566.95,907.449 1568.27,905.942 1569.59,904.433 1570.91,902.922 1572.23,901.407 1573.54,899.89 1574.86,898.37 1576.18,896.848 1577.5,895.323 1578.82,893.796 1580.14,892.265 1581.46,890.732 1582.77,889.197 1584.09,887.658 1585.41,886.117 1586.73,884.574 1588.05,883.028 1589.37,881.479 1590.68,879.927 1592,878.373 1593.32,876.816 1594.64,875.257 1595.96,873.694 1597.28,872.129 1598.6,870.562 1599.91,868.992 1601.23,867.419 1602.55,865.843 1603.87,864.265 1605.19,862.684 1606.51,861.101 1607.83,859.514 1609.14,857.926 1610.46,856.334 1611.78,854.74 1613.1,853.143 1614.42,851.543 1615.74,849.941 1617.06,848.336 1618.37,846.729 1619.69,845.119 1621.01,843.506 1622.33,841.89 1623.65,840.272 1624.97,838.651 1626.29,837.027 1627.6,835.401 1628.92,833.772 1630.24,832.141 1631.56,830.506 1632.88,828.869 1634.2,827.23 1635.51,825.587 1636.83,823.942 1638.15,822.295 1639.47,820.644 1640.79,818.991 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894.501,1350.84 895.819,1350.54 897.138,1350.23 898.456,1349.93 899.775,1349.62 901.093,1349.31 902.412,1349 903.731,1348.68 905.049,1348.37 906.368,1348.05 907.686,1347.73 909.005,1347.41 910.323,1347.09 911.642,1346.76 912.96,1346.44 914.279,1346.11 915.597,1345.78 916.916,1345.45 918.234,1345.11 919.553,1344.78 920.871,1344.44 922.19,1344.1 923.508,1343.76 924.827,1343.41 926.146,1343.07 927.464,1342.72 928.783,1342.37 930.101,1342.02 931.42,1341.67 932.738,1341.31 934.057,1340.96 935.375,1340.6 936.694,1340.24 938.012,1339.88 939.331,1339.51 940.649,1339.15 941.968,1338.78 943.286,1338.41 944.605,1338.04 945.923,1337.66 947.242,1337.29 948.561,1336.91 949.879,1336.53 951.198,1336.15 952.516,1335.77 953.835,1335.38 955.153,1334.99 956.472,1334.6 957.79,1334.21 959.109,1333.82 960.427,1333.42 961.746,1333.03 963.064,1332.63 964.383,1332.23 965.701,1331.82 967.02,1331.42 968.338,1331.01 969.657,1330.6 970.976,1330.19 972.294,1329.78 973.613,1329.36 974.931,1328.95 976.25,1328.53 977.568,1328.11 978.887,1327.68 980.205,1327.26 981.524,1326.83 982.842,1326.4 984.161,1325.97 985.479,1325.54 986.798,1325.1 988.116,1324.67 989.435,1324.23 990.754,1323.79 992.072,1323.34 993.391,1322.9 994.709,1322.45 996.028,1322 997.346,1321.55 998.665,1321.09 999.983,1320.64 1001.3,1320.18 1002.62,1319.72 1003.94,1319.26 1005.26,1318.8 1006.58,1318.33 1007.89,1317.86 1009.21,1317.39 1010.53,1316.92 1011.85,1316.44 1013.17,1315.97 1014.49,1315.49 1015.81,1315.01 1017.12,1314.53 1018.44,1314.04 1019.76,1313.55 1021.08,1313.07 1022.4,1312.57 1023.72,1312.08 1025.04,1311.59 1026.35,1311.09 1027.67,1310.59 1028.99,1310.09 1030.31,1309.58 1031.63,1309.08 1032.95,1308.57 1034.27,1308.06 1035.58,1307.55 1036.9,1307.03 1038.22,1306.52 1039.54,1306 1040.86,1305.48 1042.18,1304.95 1043.49,1304.43 1044.81,1303.9 1046.13,1303.37 1047.45,1302.84 1048.77,1302.3 1050.09,1301.77 1051.41,1301.23 1052.72,1300.69 1054.04,1300.15 1055.36,1299.6 1056.68,1299.06 1058,1298.51 1059.32,1297.96 1060.64,1297.4 1061.95,1296.85 1063.27,1296.29 1064.59,1295.73 1065.91,1295.17 1067.23,1294.6 1068.55,1294.04 1069.87,1293.47 1071.18,1292.9 1072.5,1292.32 1073.82,1291.75 1075.14,1291.17 1076.46,1290.59 1077.78,1290.01 1079.1,1289.42 1080.41,1288.84 1081.73,1288.25 1083.05,1287.66 1084.37,1287.06 1085.69,1286.47 1087.01,1285.87 1088.32,1285.27 1089.64,1284.67 1090.96,1284.06 1092.28,1283.46 1093.6,1282.85 1094.92,1282.24 1096.24,1281.63 1097.55,1281.01 1098.87,1280.39 1100.19,1279.77 1101.51,1279.15 1102.83,1278.53 1104.15,1277.9 1105.47,1277.27 1106.78,1276.64 1108.1,1276 1109.42,1275.37 1110.74,1274.73 1112.06,1274.09 1113.38,1273.45 1114.7,1272.8 1116.01,1272.16 1117.33,1271.51 1118.65,1270.85 1119.97,1270.2 1121.29,1269.54 1122.61,1268.89 1123.93,1268.22 1125.24,1267.56 1126.56,1266.9 1127.88,1266.23 1129.2,1265.56 1130.52,1264.89 1131.84,1264.21 1133.15,1263.53 1134.47,1262.86 1135.79,1262.17 1137.11,1261.49 1138.43,1260.8 1139.75,1260.12 1141.07,1259.42 1142.38,1258.73 1143.7,1258.04 1145.02,1257.34 1146.34,1256.64 1147.66,1255.94 1148.98,1255.23 1150.3,1254.52 1151.61,1253.81 1152.93,1253.1 1154.25,1252.39 1155.57,1251.67 1156.89,1250.95 1158.21,1250.23 1159.53,1249.51 1160.84,1248.78 1162.16,1248.06 1163.48,1247.33 1164.8,1246.59 1166.12,1245.86 1167.44,1245.12 1168.76,1244.38 1170.07,1243.64 1171.39,1242.89 1172.71,1242.15 1174.03,1241.4 1175.35,1240.65 1176.67,1239.89 1177.98,1239.14 1179.3,1238.38 1180.62,1237.62 1181.94,1236.85 1183.26,1236.09 1184.58,1235.32 1185.9,1234.55 1187.21,1233.78 1188.53,1233 1189.85,1232.22 1191.17,1231.44 1192.49,1230.66 1193.81,1229.88 1195.13,1229.09 1196.44,1228.3 1197.76,1227.51 1199.08,1226.71 1200.4,1225.92 1201.72,1225.12 1203.04,1224.32 1204.36,1223.51 1205.67,1222.71 1206.99,1221.9 1208.31,1221.09 1209.63,1220.27 1210.95,1219.46 1212.27,1218.64 1213.59,1217.82 1214.9,1216.99 1216.22,1216.17 1217.54,1215.34 1218.86,1214.51 1220.18,1213.68 1221.5,1212.84 1222.81,1212.01 1224.13,1211.17 1225.45,1210.32 1226.77,1209.48 1228.09,1208.63 1229.41,1207.78 1230.73,1206.93 1232.04,1206.07 1233.36,1205.22 1234.68,1204.36 1236,1203.5 1237.32,1202.63 1238.64,1201.77 1239.96,1200.9 1241.27,1200.03 1242.59,1199.15 1243.91,1198.28 1245.23,1197.4 1246.55,1196.52 1247.87,1195.63 1249.19,1194.75 1250.5,1193.86 1251.82,1192.97 1253.14,1192.07 1254.46,1191.18 1255.78,1190.28 1257.1,1189.38 1258.42,1188.47 1259.73,1187.57 1261.05,1186.66 1262.37,1185.75 1263.69,1184.84 1265.01,1183.92 1266.33,1183 1267.64,1182.08 1268.96,1181.16 1270.28,1180.23 1271.6,1179.31 1272.92,1178.38 1274.24,1177.44 1275.56,1176.51 1276.87,1175.57 1278.19,1174.63 1279.51,1173.69 1280.83,1172.74 1282.15,1171.79 1283.47,1170.84 1284.79,1169.89 1286.1,1168.94 1287.42,1167.98 1288.74,1167.02 1290.06,1166.06 1291.38,1165.09 1292.7,1164.12 1294.02,1163.15 1295.33,1162.18 1296.65,1161.21 1297.97,1160.23 1299.29,1159.25 1300.61,1158.27 1301.93,1157.28 1303.25,1156.3 1304.56,1155.31 1305.88,1154.31 1307.2,1153.32 1308.52,1152.32 1309.84,1151.32 1311.16,1150.32 1312.47,1149.31 1313.79,1148.31 1315.11,1147.3 1316.43,1146.28 1317.75,1145.27 1319.07,1144.25 1320.39,1143.23 1321.7,1142.21 1323.02,1141.19 1324.34,1140.16 1325.66,1139.13 1326.98,1138.1 1328.3,1137.06 1329.62,1136.02 1330.93,1134.98 1332.25,1133.94 1333.57,1132.9 1334.89,1131.85 1336.21,1130.8 1337.53,1129.75 1338.85,1128.69 1340.16,1127.63 1341.48,1126.57 1342.8,1125.51 1344.12,1124.45 1345.44,1123.38 1346.76,1122.31 1348.08,1121.23 1349.39,1120.16 1350.71,1119.08 1352.03,1118 1353.35,1116.92 1354.67,1115.83 1355.99,1114.75 1357.3,1113.65 1358.62,1112.56 1359.94,1111.47 1361.26,1110.37 1362.58,1109.27 1363.9,1108.16 1365.22,1107.06 1366.53,1105.95 1367.85,1104.84 1369.17,1103.73 1370.49,1102.61 1371.81,1101.49 1373.13,1100.37 1374.45,1099.25 1375.76,1098.12 1377.08,1096.99 1378.4,1095.86 1379.72,1094.73 1381.04,1093.59 1382.36,1092.45 1383.68,1091.31 1384.99,1090.17 1386.31,1089.02 1387.63,1087.87 1388.95,1086.72 1390.27,1085.57 1391.59,1084.41 1392.91,1083.25 1394.22,1082.09 1395.54,1080.92 1396.86,1079.76 1398.18,1078.59 1399.5,1077.42 1400.82,1076.24 1402.14,1075.06 1403.45,1073.88 1404.77,1072.7 1406.09,1071.52 1407.41,1070.33 1408.73,1069.14 1410.05,1067.95 1411.36,1066.75 1412.68,1065.55 1414,1064.35 1415.32,1063.15 1416.64,1061.94 1417.96,1060.74 1419.28,1059.53 1420.59,1058.31 1421.91,1057.1 1423.23,1055.88 1424.55,1054.66 1425.87,1053.43 1427.19,1052.21 1428.51,1050.98 1429.82,1049.75 1431.14,1048.51 1432.46,1047.28 1433.78,1046.04 1435.1,1044.8 1436.42,1043.55 1437.74,1042.31 1439.05,1041.06 1440.37,1039.8 1441.69,1038.55 1443.01,1037.29 1444.33,1036.03 1445.65,1034.77 1446.97,1033.51 1448.28,1032.24 1449.6,1030.97 1450.92,1029.69 1452.24,1028.42 1453.56,1027.14 1454.88,1025.86 1456.19,1024.58 1457.51,1023.29 1458.83,1022 1460.15,1020.71 1461.47,1019.42 1462.79,1018.12 1464.11,1016.82 1465.42,1015.52 1466.74,1014.22 1468.06,1012.91 1469.38,1011.6 1470.7,1010.29 1472.02,1008.98 1473.34,1007.66 1474.65,1006.34 1475.97,1005.02 1477.29,1003.69 1478.61,1002.37 1479.93,1001.04 1481.25,999.703 1482.57,998.368 1483.88,997.03 1485.2,995.69 1486.52,994.347 1487.84,993.001 1489.16,991.653 1490.48,990.302 1491.8,988.948 1493.11,987.592 1494.43,986.233 1495.75,984.872 1497.07,983.508 1498.39,982.141 1499.71,980.772 1501.02,979.4 1502.34,978.025 1503.66,976.648 1504.98,975.268 1506.3,973.886 1507.62,972.501 1508.94,971.113 1510.25,969.723 1511.57,968.33 1512.89,966.935 1514.21,965.537 1515.53,964.136 1516.85,962.732 1518.17,961.326 1519.48,959.918 1520.8,958.506 1522.12,957.092 1523.44,955.676 1524.76,954.257 1526.08,952.835 1527.4,951.41 1528.71,949.983 1530.03,948.554 1531.35,947.121 1532.67,945.686 1533.99,944.249 1535.31,942.808 1536.63,941.365 1537.94,939.92 1539.26,938.472 1540.58,937.021 1541.9,935.567 1543.22,934.111 1544.54,932.652 1545.85,931.191 1547.17,929.727 1548.49,928.26 1549.81,926.791 1551.13,925.319 1552.45,923.844 1553.77,922.367 1555.08,920.887 1556.4,919.405 1557.72,917.919 1559.04,916.432 1560.36,914.941 1561.68,913.448 1563,911.952 1564.31,910.454 1565.63,908.952 1566.95,907.449 1568.27,905.942 1569.59,904.433 1570.91,902.922 1572.23,901.407 1573.54,899.89 1574.86,898.37 1576.18,896.848 1577.5,895.323 1578.82,893.796 1580.14,892.265 1581.46,890.732 1582.77,889.197 1584.09,887.658 1585.41,886.117 1586.73,884.574 1588.05,883.028 1589.37,881.479 1590.68,879.927 1592,878.373 1593.32,876.816 1594.64,875.257 1595.96,873.694 1597.28,872.129 1598.6,870.562 1599.91,868.992 1601.23,867.419 1602.55,865.843 1603.87,864.265 1605.19,862.684 1606.51,861.101 1607.83,859.514 1609.14,857.926 1610.46,856.334 1611.78,854.74 1613.1,853.143 1614.42,851.543 1615.74,849.941 1617.06,848.336 1618.37,846.729 1619.69,845.119 1621.01,843.506 1622.33,841.89 1623.65,840.272 1624.97,838.651 1626.29,837.027 1627.6,835.401 1628.92,833.772 1630.24,832.141 1631.56,830.506 1632.88,828.869 1634.2,827.23 1635.51,825.587 1636.83,823.942 1638.15,822.295 1639.47,820.644 1640.79,818.991 1642.11,817.336 1643.43,815.677 1644.74,814.016 1646.06,812.352 1647.38,810.686 1648.7,809.017 1650.02,807.345 1651.34,805.671 1652.66,803.994 1653.97,802.314 1655.29,800.631 1656.61,798.946 1657.93,797.258 1659.25,795.568 1660.57,793.874 1661.89,792.178 1663.2,790.48 1664.52,788.778 1665.84,787.074 1667.16,785.368 1668.48,783.658 1669.8,781.946 1671.12,780.231 1672.43,778.514 1673.75,776.794 1675.07,775.071 1676.39,773.346 1677.71,771.617 1679.03,769.887 1680.34,768.153 1681.66,766.417 1682.98,764.678 1684.3,762.936 1685.62,761.192 1686.94,759.445 1688.26,757.695 1689.57,755.942 1690.89,754.187 1692.21,752.429 1693.53,750.669 1694.85,748.906 1696.17,747.14 1697.49,745.371 1698.8,743.6 1700.12,741.826 1701.44,740.049 1702.76,738.27 1704.08,736.488 1705.4,734.703 1706.72,732.915 1708.03,731.125 1709.35,729.332 1710.67,727.537 1711.99,725.739 1713.31,723.938 1714.63,722.134 1715.95,720.327 1717.26,718.518 1718.58,716.707 1719.9,714.892 1721.22,713.075 1722.54,711.255 1723.86,709.432 1725.17,707.607 1726.49,705.779 1727.81,703.948 1729.13,702.115 1730.45,700.279 1731.77,698.44 1733.09,696.598 1734.4,694.754 1735.72,692.907 1737.04,691.057 1738.36,689.205 1739.68,687.35 1741,685.492 1742.32,683.632 1743.63,681.768 1744.95,679.902 1746.27,678.034 1747.59,676.162 1748.91,674.288 1750.23,672.412 1751.55,670.532 1752.86,668.65 1754.18,666.765 1755.5,664.877 1756.82,662.987 1758.14,661.094 1759.46,659.198 1760.78,657.3 1762.09,655.399 1763.41,653.495 1764.73,651.588 1766.05,649.679 1767.37,647.767 1768.69,645.852 1770.01,643.935 1771.32,642.014 1772.64,640.092 1773.96,638.166 1775.28,636.238 1776.6,634.306 1777.92,632.373 1779.23,630.436 1780.55,628.497 1781.87,626.555 1783.19,624.61 1784.51,622.663 1785.83,620.713 1787.15,618.76 1788.46,616.805 1789.78,614.846 1791.1,612.885 1792.42,610.922 1793.74,608.955 1795.06,606.986 1796.38,605.014 1797.69,603.04 1799.01,601.062 1800.33,599.082 1801.65,597.1 1802.97,595.114 1804.29,593.126 1805.61,591.135 1806.92,589.141 1808.24,587.145 1809.56,585.146 1810.88,583.144 1812.2,581.14 1813.52,579.132 1814.84,577.122 1816.15,575.11 1817.47,573.094 1818.79,571.076 1820.11,569.055 1821.43,567.031 1822.75,565.005 1824.06,562.976 1825.38,560.944 1826.7,558.91 1828.02,556.872 1829.34,554.832 1830.66,552.79 1831.98,550.744 1833.29,548.696 1834.61,546.645 1835.93,544.591 1837.25,542.535 1838.57,540.476 1839.89,538.414 1841.21,536.349 1842.52,534.282 1843.84,532.212 1845.16,530.139 1846.48,528.064 1847.8,525.985 1849.12,523.904 1850.44,521.821 1851.75,519.734 1853.07,517.645 1854.39,515.553 1855.71,513.459 1857.03,511.361 1858.35,509.261 1859.67,507.158 1860.98,505.053 1862.3,502.944 1863.62,500.833 1864.94,498.719 1866.26,496.603 1867.58,494.484 1868.89,492.361 1870.21,490.237 1871.53,488.109 1872.85,485.979 1874.17,483.846 1875.49,481.71 1876.81,479.572 1878.12,477.431 1879.44,475.287 1880.76,473.14 1882.08,470.991 1883.4,468.838 1884.72,466.684 1886.04,464.526 1887.35,462.366 1888.67,460.202 1889.99,458.037 1891.31,455.868 1892.63,453.697 1893.95,451.523 1895.27,449.346 1896.58,447.166 1897.9,444.984 1899.22,442.799 1900.54,440.611 1901.86,438.42 1903.18,436.227 1904.5,434.031 1905.81,431.832 1907.13,429.631 1908.45,427.427 1909.77,425.22 1911.09,423.01 1912.41,420.797 1913.72,418.582 1915.04,416.364 1916.36,414.143 1917.68,411.92 1919,409.694 1920.32,407.465 1921.64,405.233 1922.95,402.998 1924.27,400.761 1925.59,398.521 1926.91,396.278 1928.23,394.033 1929.55,391.785 1930.87,389.534 1932.18,387.28 1933.5,385.024 1934.82,382.764 1936.14,380.502 1937.46,378.238 1938.78,375.97 1940.1,373.7 1941.41,371.427 1942.73,369.151 1944.05,366.873 1945.37,364.592 1946.69,362.308 1948.01,360.021 1949.33,357.731 1950.64,355.439 1951.96,353.144 1953.28,350.846 1954.6,348.546 1955.92,346.243 1957.24,343.937 1958.55,341.628 1959.87,339.316 1961.19,337.002 1962.51,334.685 1963.83,332.365 1965.15,330.043 1966.47,327.718 1967.78,325.39 1969.1,323.059 1970.42,320.725 1971.74,318.389 1973.06,316.05 1974.38,313.708 1975.7,311.364 1977.01,309.016 1978.33,306.666 1979.65,304.313 1980.97,301.958 1982.29,299.599 1983.61,297.238 1984.93,294.874 1986.24,292.508 1987.56,290.138 1988.88,287.766 1990.2,285.391 1991.52,283.014 1992.84,280.633 1994.16,278.25 1995.47,275.864 1996.79,273.476 1998.11,271.084 1999.43,268.69 2000.75,266.293 2002.07,263.893 2003.38,261.491 2004.7,259.085 2006.02,256.677 2007.34,254.267 2008.66,251.853 2009.98,249.437 2011.3,247.018 2012.61,244.596 2013.93,242.171 2015.25,239.744 2016.57,237.314 2017.89,234.881 2019.21,232.445 2020.53,230.007 2021.84,227.566 2023.16,225.122 2024.48,222.675 2025.8,220.226 2027.12,217.773 2028.44,215.319 2029.76,212.861 2031.07,210.4 2032.39,207.937 2033.71,205.471 2035.03,203.002 2036.35,200.531 2037.67,198.056 2038.99,195.579 2040.3,193.099 2041.62,190.617 2042.94,188.131 2044.26,185.643 2045.58,183.152 2046.9,180.659 2048.21,178.162 2049.53,175.663 2050.85,173.161 2052.17,170.656 2053.49,168.149 2054.81,165.638 2056.13,163.125 2057.44,160.609 2058.76,158.091 2060.08,155.569 2061.4,153.045 2062.72,150.518 2064.04,147.989 2065.36,145.456 2066.67,142.921 2067.99,140.383 2069.31,137.842 2070.63,135.299 2071.95,132.752 2073.27,130.203 2074.59,127.652 2075.9,125.097 2077.22,122.54 2078.54,119.979 2079.86,117.417 2081.18,114.851 2082.5,112.282 2083.82,109.711 2085.13,107.137 2086.45,104.56 2087.77,101.981 2089.09,99.3986 2090.41,96.8135 2091.73,94.2256 2093.04,91.635 2094.36,89.0416 2095.68,86.4454 2097,86.1857 2098.32,86.1857 2099.64,86.1857 2100.96,86.1857 2102.27,86.1857 2103.59,86.1857 2104.91,86.1857 2106.23,86.1857 2107.55,86.1857 2108.87,86.1857 2110.19,86.1857 2111.5,86.1857 2112.82,86.1857 2114.14,86.1857 2115.46,86.1857 2116.78,86.1857 2118.1,86.1857 2119.42,86.1857 2120.73,86.1857 2122.05,86.1857 2123.37,86.1857 2124.69,86.1857 2126.01,86.1857 2127.33,86.1857 2128.65,86.1857 2129.96,86.1857 2131.28,86.1857 2132.6,86.1857 2133.92,86.1857 2135.24,86.1857 2136.56,86.1857 2137.87,86.1857 2139.19,86.1857 2140.51,86.1857 2141.83,86.1857 2143.15,86.1857 2144.47,86.1857 2145.79,86.1857 2147.1,86.1857 2148.42,86.1857 2149.74,86.1857 2151.06,86.1857 2152.38,86.1857 2153.7,86.1857 2155.02,86.1857 2156.33,86.1857 2157.65,86.1857 2158.97,86.1857 2160.29,86.1857 2161.61,86.1857 2162.93,86.1857 2164.25,86.1857 2165.56,86.1857 2166.88,86.1857 2168.2,86.1857 2169.52,86.1857 2170.84,86.1857 2172.16,86.1857 2173.48,86.1857 2174.79,86.1857 2176.11,86.1857 2177.43,86.1857 2178.75,86.1857 2180.07,86.1857 2181.39,86.1857 2182.71,86.1857 2184.02,86.1857 2185.34,86.1857 2186.66,86.1857 2187.98,86.1857 2189.3,86.1857 2190.62,86.1857 2191.93,86.1857 2193.25,86.1857 2194.57,86.1857 2195.89,86.1857 2197.21,86.1857 2198.53,86.1857 2199.85,86.1857 2201.16,86.1857 2202.48,86.1857 2203.8,86.1857 2205.12,86.1857 2206.44,86.1857 2207.76,86.1857 2209.08,86.1857 2210.39,86.1857 2211.71,86.1857 2213.03,86.1857 2214.35,86.1857 2215.67,86.1857 2216.99,86.1857 2218.31,86.1857 2219.62,86.1857 2220.94,86.1857 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"<path clip-path=\"url(#clip560)\" d=\"M527.596 164.636 Q525.791 169.266 524.078 170.678 Q522.365 172.09 519.494 172.09 L516.092 172.09 L516.092 168.525 L518.592 168.525 Q520.351 168.525 521.323 167.692 Q522.295 166.858 523.476 163.756 L524.24 161.812 L513.754 136.303 L518.268 136.303 L526.369 156.581 L534.471 136.303 L538.985 136.303 L527.596 164.636 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip560)\" d=\"M546.277 158.293 L553.916 158.293 L553.916 131.928 L545.605 133.595 L545.605 129.335 L553.869 127.669 L558.545 127.669 L558.545 158.293 L566.184 158.293 L566.184 162.229 L546.277 162.229 L546.277 158.293 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"internal_energy(m) = - 0.5 * z * m .^ 2\n",
"\n",
"plot(temperatures, internal_energy.(moments), xlabel=L\"T\", ylabel=L\"U/N\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Entropy\n",
"$S = - N k_\\mathrm{B}[\\left(\\frac{1}{2} + m \\right) \\log \\left(\\frac{1}{2} + m \\right) + \\left(\\frac{1}{2} - m \\right) \\log \\left(\\frac{1}{2} - m \\right) ]$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
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998.38,1246.3 999.723,1245.53 1001.06,1244.75 1002.41,1243.96 1003.75,1243.18 1005.09,1242.39 1006.43,1241.6 1007.78,1240.81 1009.12,1240.02 1010.46,1239.22 1011.8,1238.42 1013.15,1237.62 1014.49,1236.82 1015.83,1236.02 1017.17,1235.21 1018.52,1234.4 1019.86,1233.59 1021.2,1232.78 1022.54,1231.96 1023.88,1231.15 1025.23,1230.33 1026.57,1229.5 1027.91,1228.68 1029.25,1227.85 1030.6,1227.03 1031.94,1226.2 1033.28,1225.36 1034.62,1224.53 1035.97,1223.69 1037.31,1222.85 1038.65,1222.01 1039.99,1221.17 1041.33,1220.32 1042.68,1219.48 1044.02,1218.63 1045.36,1217.78 1046.7,1216.92 1048.05,1216.07 1049.39,1215.21 1050.73,1214.35 1052.07,1213.49 1053.42,1212.62 1054.76,1211.76 1056.1,1210.89 1057.44,1210.02 1058.79,1209.14 1060.13,1208.27 1061.47,1207.39 1062.81,1206.51 1064.15,1205.63 1065.5,1204.75 1066.84,1203.86 1068.18,1202.98 1069.52,1202.09 1070.87,1201.2 1072.21,1200.3 1073.55,1199.41 1074.89,1198.51 1076.24,1197.61 1077.58,1196.71 1078.92,1195.8 1080.26,1194.9 1081.61,1193.99 1082.95,1193.08 1084.29,1192.17 1085.63,1191.25 1086.97,1190.34 1088.32,1189.42 1089.66,1188.5 1091,1187.58 1092.34,1186.65 1093.69,1185.72 1095.03,1184.8 1096.37,1183.87 1097.71,1182.93 1099.06,1182 1100.4,1181.06 1101.74,1180.12 1103.08,1179.18 1104.42,1178.24 1105.77,1177.3 1107.11,1176.35 1108.45,1175.4 1109.79,1174.45 1111.14,1173.5 1112.48,1172.54 1113.82,1171.59 1115.16,1170.63 1116.51,1169.67 1117.85,1168.7 1119.19,1167.74 1120.53,1166.77 1121.88,1165.81 1123.22,1164.83 1124.56,1163.86 1125.9,1162.89 1127.24,1161.91 1128.59,1160.93 1129.93,1159.95 1131.27,1158.97 1132.61,1157.99 1133.96,1157 1135.3,1156.01 1136.64,1155.02 1137.98,1154.03 1139.33,1153.04 1140.67,1152.04 1142.01,1151.04 1143.35,1150.04 1144.69,1149.04 1146.04,1148.04 1147.38,1147.03 1148.72,1146.02 1150.06,1145.01 1151.41,1144 1152.75,1142.99 1154.09,1141.97 1155.43,1140.96 1156.78,1139.94 1158.12,1138.92 1159.46,1137.89 1160.8,1136.87 1162.15,1135.84 1163.49,1134.81 1164.83,1133.78 1166.17,1132.75 1167.51,1131.71 1168.86,1130.68 1170.2,1129.64 1171.54,1128.6 1172.88,1127.56 1174.23,1126.51 1175.57,1125.47 1176.91,1124.42 1178.25,1123.37 1179.6,1122.32 1180.94,1121.27 1182.28,1120.21 1183.62,1119.15 1184.96,1118.1 1186.31,1117.04 1187.65,1115.97 1188.99,1114.91 1190.33,1113.84 1191.68,1112.77 1193.02,1111.7 1194.36,1110.63 1195.7,1109.56 1197.05,1108.48 1198.39,1107.41 1199.73,1106.33 1201.07,1105.25 1202.42,1104.16 1203.76,1103.08 1205.1,1101.99 1206.44,1100.9 1207.78,1099.81 1209.13,1098.72 1210.47,1097.63 1211.81,1096.53 1213.15,1095.44 1214.5,1094.34 1215.84,1093.24 1217.18,1092.13 1218.52,1091.03 1219.87,1089.92 1221.21,1088.81 1222.55,1087.7 1223.89,1086.59 1225.23,1085.48 1226.58,1084.36 1227.92,1083.25 1229.26,1082.13 1230.6,1081.01 1231.95,1079.89 1233.29,1078.76 1234.63,1077.63 1235.97,1076.51 1237.32,1075.38 1238.66,1074.25 1240,1073.11 1241.34,1071.98 1242.69,1070.84 1244.03,1069.7 1245.37,1068.56 1246.71,1067.42 1248.05,1066.28 1249.4,1065.13 1250.74,1063.99 1252.08,1062.84 1253.42,1061.69 1254.77,1060.54 1256.11,1059.38 1257.45,1058.23 1258.79,1057.07 1260.14,1055.91 1261.48,1054.75 1262.82,1053.59 1264.16,1052.42 1265.5,1051.26 1266.85,1050.09 1268.19,1048.92 1269.53,1047.75 1270.87,1046.58 1272.22,1045.4 1273.56,1044.22 1274.9,1043.05 1276.24,1041.87 1277.59,1040.69 1278.93,1039.5 1280.27,1038.32 1281.61,1037.13 1282.96,1035.94 1284.3,1034.75 1285.64,1033.56 1286.98,1032.37 1288.32,1031.18 1289.67,1029.98 1291.01,1028.78 1292.35,1027.58 1293.69,1026.38 1295.04,1025.18 1296.38,1023.97 1297.72,1022.77 1299.06,1021.56 1300.41,1020.35 1301.75,1019.14 1303.09,1017.92 1304.43,1016.71 1305.77,1015.49 1307.12,1014.28 1308.46,1013.06 1309.8,1011.83 1311.14,1010.61 1312.49,1009.39 1313.83,1008.16 1315.17,1006.93 1316.51,1005.7 1317.86,1004.47 1319.2,1003.24 1320.54,1002.01 1321.88,1000.77 1323.23,999.534 1324.57,998.295 1325.91,997.054 1327.25,995.812 1328.59,994.568 1329.94,993.323 1331.28,992.076 1332.62,990.827 1333.96,989.577 1335.31,988.325 1336.65,987.072 1337.99,985.817 1339.33,984.56 1340.68,983.302 1342.02,982.043 1343.36,980.781 1344.7,979.518 1346.04,978.254 1347.39,976.988 1348.73,975.72 1350.07,974.451 1351.41,973.181 1352.76,971.908 1354.1,970.635 1355.44,969.359 1356.78,968.082 1358.13,966.804 1359.47,965.524 1360.81,964.242 1362.15,962.959 1363.5,961.675 1364.84,960.388 1366.18,959.101 1367.52,957.811 1368.86,956.52 1370.21,955.228 1371.55,953.934 1372.89,952.639 1374.23,951.342 1375.58,950.043 1376.92,948.743 1378.26,947.442 1379.6,946.139 1380.95,944.834 1382.29,943.528 1383.63,942.221 1384.97,940.912 1386.32,939.601 1387.66,938.289 1389,936.976 1390.34,935.66 1391.68,934.344 1393.03,933.026 1394.37,931.706 1395.71,930.385 1397.05,929.063 1398.4,927.739 1399.74,926.413 1401.08,925.086 1402.42,923.758 1403.77,922.428 1405.11,921.096 1406.45,919.763 1407.79,918.429 1409.13,917.093 1410.48,915.756 1411.82,914.417 1413.16,913.077 1414.5,911.735 1415.85,910.392 1417.19,909.047 1418.53,907.701 1419.87,906.353 1421.22,905.004 1422.56,903.654 1423.9,902.302 1425.24,900.949 1426.59,899.594 1427.93,898.238 1429.27,896.88 1430.61,895.521 1431.95,894.16 1433.3,892.798 1434.64,891.435 1435.98,890.07 1437.32,888.704 1438.67,887.336 1440.01,885.967 1441.35,884.597 1442.69,883.225 1444.04,881.851 1445.38,880.476 1446.72,879.1 1448.06,877.723 1449.4,876.344 1450.75,874.963 1452.09,873.581 1453.43,872.198 1454.77,870.814 1456.12,869.428 1457.46,868.04 1458.8,866.651 1460.14,865.261 1461.49,863.869 1462.83,862.476 1464.17,861.082 1465.51,859.686 1466.86,858.289 1468.2,856.891 1469.54,855.491 1470.88,854.089 1472.22,852.687 1473.57,851.283 1474.91,849.877 1476.25,848.471 1477.59,847.062 1478.94,845.653 1480.28,844.242 1481.62,842.83 1482.96,841.416 1484.31,840.001 1485.65,838.585 1486.99,837.167 1488.33,835.748 1489.67,834.328 1491.02,832.906 1492.36,831.483 1493.7,830.059 1495.04,828.633 1496.39,827.206 1497.73,825.778 1499.07,824.348 1500.41,822.917 1501.76,821.484 1503.1,820.051 1504.44,818.616 1505.78,817.179 1507.13,815.741 1508.47,814.302 1509.81,812.862 1511.15,811.42 1512.49,809.977 1513.84,808.533 1515.18,807.087 1516.52,805.64 1517.86,804.192 1519.21,802.742 1520.55,801.292 1521.89,799.839 1523.23,798.386 1524.58,796.931 1525.92,795.475 1527.26,794.018 1528.6,792.559 1529.94,791.099 1531.29,789.638 1532.63,788.175 1533.97,786.711 1535.31,785.246 1536.66,783.78 1538,782.312 1539.34,780.843 1540.68,779.373 1542.03,777.901 1543.37,776.428 1544.71,774.954 1546.05,773.479 1547.4,772.002 1548.74,770.524 1550.08,769.045 1551.42,767.565 1552.76,766.083 1554.11,764.6 1555.45,763.116 1556.79,761.631 1558.13,760.144 1559.48,758.656 1560.82,757.167 1562.16,755.676 1563.5,754.184 1564.85,752.691 1566.19,751.197 1567.53,749.702 1568.87,748.205 1570.21,746.707 1571.56,745.208 1572.9,743.707 1574.24,742.206 1575.58,740.703 1576.93,739.199 1578.27,737.693 1579.61,736.187 1580.95,734.679 1582.3,733.17 1583.64,731.66 1584.98,730.148 1586.32,728.635 1587.67,727.122 1589.01,725.606 1590.35,724.09 1591.69,722.572 1593.03,721.054 1594.38,719.534 1595.72,718.012 1597.06,716.49 1598.4,714.966 1599.75,713.442 1601.09,711.916 1602.43,710.388 1603.77,708.86 1605.12,707.33 1606.46,705.8 1607.8,704.268 1609.14,702.734 1610.48,701.2 1611.83,699.664 1613.17,698.128 1614.51,696.59 1615.85,695.051 1617.2,693.51 1618.54,691.969 1619.88,690.426 1621.22,688.882 1622.57,687.337 1623.91,685.791 1625.25,684.244 1626.59,682.695 1627.94,681.146 1629.28,679.595 1630.62,678.043 1631.96,676.49 1633.3,674.935 1634.65,673.38 1635.99,671.823 1637.33,670.265 1638.67,668.706 1640.02,667.146 1641.36,665.585 1642.7,664.022 1644.04,662.459 1645.39,660.894 1646.73,659.328 1648.07,657.761 1649.41,656.193 1650.76,654.624 1652.1,653.053 1653.44,651.482 1654.78,649.909 1656.12,648.335 1657.47,646.76 1658.81,645.184 1660.15,643.607 1661.49,642.028 1662.84,640.449 1664.18,638.868 1665.52,637.286 1666.86,635.703 1668.21,634.119 1669.55,632.534 1670.89,630.948 1672.23,629.361 1673.57,627.772 1674.92,626.183 1676.26,624.592 1677.6,623 1678.94,621.407 1680.29,619.813 1681.63,618.218 1682.97,616.622 1684.31,615.024 1685.66,613.426 1687,611.826 1688.34,610.226 1689.68,608.624 1691.03,607.021 1692.37,605.417 1693.71,603.812 1695.05,602.206 1696.39,600.599 1697.74,598.99 1699.08,597.381 1700.42,595.77 1701.76,594.159 1703.11,592.546 1704.45,590.933 1705.79,589.318 1707.13,587.702 1708.48,586.085 1709.82,584.467 1711.16,582.848 1712.5,581.228 1713.84,579.606 1715.19,577.984 1716.53,576.361 1717.87,574.736 1719.21,573.111 1720.56,571.484 1721.9,569.856 1723.24,568.228 1724.58,566.598 1725.93,564.967 1727.27,563.335 1728.61,561.702 1729.95,560.068 1731.3,558.433 1732.64,556.797 1733.98,555.16 1735.32,553.522 1736.66,551.882 1738.01,550.242 1739.35,548.601 1740.69,546.958 1742.03,545.315 1743.38,543.671 1744.72,542.025 1746.06,540.379 1747.4,538.731 1748.75,537.082 1750.09,535.433 1751.43,533.782 1752.77,532.13 1754.11,530.478 1755.46,528.824 1756.8,527.169 1758.14,525.513 1759.48,523.856 1760.83,522.199 1762.17,520.54 1763.51,518.88 1764.85,517.219 1766.2,515.557 1767.54,513.894 1768.88,512.23 1770.22,510.565 1771.57,508.899 1772.91,507.232 1774.25,505.564 1775.59,503.895 1776.93,502.225 1778.28,500.554 1779.62,498.882 1780.96,497.209 1782.3,495.535 1783.65,493.86 1784.99,492.184 1786.33,490.507 1787.67,488.829 1789.02,487.15 1790.36,485.47 1791.7,483.789 1793.04,482.107 1794.38,480.424 1795.73,478.74 1797.07,477.055 1798.41,475.369 1799.75,473.682 1801.1,471.994 1802.44,470.305 1803.78,468.615 1805.12,466.925 1806.47,465.233 1807.81,463.54 1809.15,461.846 1810.49,460.151 1811.84,458.456 1813.18,456.759 1814.52,455.061 1815.86,453.363 1817.2,451.663 1818.55,449.963 1819.89,448.261 1821.23,446.559 1822.57,444.855 1823.92,443.151 1825.26,441.445 1826.6,439.739 1827.94,438.032 1829.29,436.323 1830.63,434.614 1831.97,432.904 1833.31,431.193 1834.65,429.481 1836,427.768 1837.34,426.054 1838.68,424.339 1840.02,422.623 1841.37,420.906 1842.71,419.189 1844.05,417.47 1845.39,415.75 1846.74,414.03 1848.08,412.308 1849.42,410.586 1850.76,408.862 1852.11,407.138 1853.45,405.413 1854.79,403.687 1856.13,401.96 1857.47,400.232 1858.82,398.503 1860.16,396.773 1861.5,395.042 1862.84,393.31 1864.19,391.577 1865.53,389.844 1866.87,388.109 1868.21,386.374 1869.56,384.637 1870.9,382.9 1872.24,381.162 1873.58,379.423 1874.92,377.683 1876.27,375.942 1877.61,374.2 1878.95,372.457 1880.29,370.714 1881.64,368.969 1882.98,367.223 1884.32,365.477 1885.66,363.73 1887.01,361.981 1888.35,360.232 1889.69,358.482 1891.03,356.731 1892.38,354.98 1893.72,353.227 1895.06,351.473 1896.4,349.719 1897.74,347.963 1899.09,346.207 1900.43,344.45 1901.77,342.692 1903.11,340.933 1904.46,339.173 1905.8,337.412 1907.14,335.65 1908.48,333.888 1909.83,332.124 1911.17,330.36 1912.51,328.595 1913.85,326.829 1915.19,325.062 1916.54,323.294 1917.88,321.525 1919.22,319.756 1920.56,317.985 1921.91,316.214 1923.25,314.442 1924.59,312.669 1925.93,310.895 1927.28,309.12 1928.62,307.344 1929.96,305.567 1931.3,303.79 1932.65,302.012 1933.99,300.232 1935.33,298.452 1936.67,296.672 1938.01,294.89 1939.36,293.107 1940.7,291.324 1942.04,289.539 1943.38,287.754 1944.73,285.968 1946.07,284.181 1947.41,282.393 1948.75,280.605 1950.1,278.815 1951.44,277.025 1952.78,275.234 1954.12,273.442 1955.47,271.649 1956.81,269.855 1958.15,268.06 1959.49,266.265 1960.83,264.469 1962.18,262.672 1963.52,260.874 1964.86,259.075 1966.2,257.275 1967.55,255.475 1968.89,253.673 1970.23,251.871 1971.57,250.068 1972.92,248.264 1974.26,246.46 1975.6,244.654 1976.94,242.848 1978.28,241.041 1979.63,239.233 1980.97,237.424 1982.31,235.614 1983.65,233.804 1985,231.992 1986.34,230.18 1987.68,228.367 1989.02,226.554 1990.37,224.739 1991.71,222.924 1993.05,221.107 1994.39,219.29 1995.74,217.472 1997.08,215.654 1998.42,213.834 1999.76,212.014 2001.1,210.193 2002.45,208.371 2003.79,206.548 2005.13,204.725 2006.47,202.9 2007.82,201.075 2009.16,199.249 2010.5,197.422 2011.84,195.595 2013.19,193.766 2014.53,191.937 2015.87,190.107 2017.21,188.276 2018.55,186.444 2019.9,184.612 2021.24,182.779 2022.58,180.945 2023.92,179.11 2025.27,177.274 2026.61,175.438 2027.95,173.601 2029.29,171.763 2030.64,169.924 2031.98,168.084 2033.32,166.244 2034.66,164.403 2036.01,162.561 2037.35,160.718 2038.69,158.875 2040.03,157.03 2041.37,155.185 2042.72,153.339 2044.06,151.493 2045.4,149.645 2046.74,147.797 2048.09,145.948 2049.43,144.098 2050.77,142.248 2052.11,140.396 2053.46,138.544 2054.8,136.691 2056.14,134.837 2057.48,132.983 2058.82,131.128 2060.17,129.272 2061.51,127.415 2062.85,125.558 2064.19,123.699 2065.54,121.84 2066.88,119.98 2068.22,118.12 2069.56,116.258 2070.91,114.396 2072.25,112.533 2073.59,110.67 2074.93,108.805 2076.28,106.94 2077.62,105.074 2078.96,103.207 2080.3,101.34 2081.64,99.4717 2082.99,97.6027 2084.33,95.733 2085.67,93.8625 2087.01,91.9913 2088.36,90.1193 2089.7,88.2466 2091.04,86.3731 2092.38,86.1857 2093.73,86.1857 2095.07,86.1857 2096.41,86.1857 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1928.62,307.344 1929.96,305.567 1931.3,303.79 1932.65,302.012 1933.99,300.232 1935.33,298.452 1936.67,296.672 1938.01,294.89 1939.36,293.107 1940.7,291.324 1942.04,289.539 1943.38,287.754 1944.73,285.968 1946.07,284.181 1947.41,282.393 1948.75,280.605 1950.1,278.815 1951.44,277.025 1952.78,275.234 1954.12,273.442 1955.47,271.649 1956.81,269.855 1958.15,268.06 1959.49,266.265 1960.83,264.469 1962.18,262.672 1963.52,260.874 1964.86,259.075 1966.2,257.275 1967.55,255.475 1968.89,253.673 1970.23,251.871 1971.57,250.068 1972.92,248.264 1974.26,246.46 1975.6,244.654 1976.94,242.848 1978.28,241.041 1979.63,239.233 1980.97,237.424 1982.31,235.614 1983.65,233.804 1985,231.992 1986.34,230.18 1987.68,228.367 1989.02,226.554 1990.37,224.739 1991.71,222.924 1993.05,221.107 1994.39,219.29 1995.74,217.472 1997.08,215.654 1998.42,213.834 1999.76,212.014 2001.1,210.193 2002.45,208.371 2003.79,206.548 2005.13,204.725 2006.47,202.9 2007.82,201.075 2009.16,199.249 2010.5,197.422 2011.84,195.595 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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"entropy(m) = - (0.5 + m) * log(0.5 + m) - (0.5 - m) * log(0.5 - m)\n",
"\n",
"plot(temperatures, entropy.(moments), xlabel=L\"T\", ylabel=L\"S/N\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Free energy (as a function of $T$)\n",
"\n",
"$F = U - TS$"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"free_energy(temperature, m) = internal_energy(m) - temperature * entropy(m)\n",
"\n",
"plot(temperatures, free_energy.(temperatures, moments), xlabel=L\"T\", ylabel=L\"F/N\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Free energy (as a function of $m$)\n",
"\n",
"$F(m, T) = -\\frac{JNz}{2}m^2 + N k_\\mathrm{B} T [\\left(\\frac{1}{2} + m \\right) \\log \\left(\\frac{1}{2} + m \\right) + \\left(\\frac{1}{2} - m \\right) \\log \\left(\\frac{1}{2} - m \\right) ]$"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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