{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Modèle d'Ising\n", "\n", "Un système magnétique peut-être décrit de façon simple avec l'Hamiltonien suivant (modèle d'Heisenberg):\n", "\\begin{equation}\n", " H = -\\frac{4}{h^2}\\sum_{i.5) - 1\n", " return ini_state" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "ini_state = create_initial_state(N)\n", "out_stateA, _ = metropolis(ini_state, beta=1, M=1000)\n", "out_stateB, _ = metropolis(ini_state, beta=1, M=1000000)\n", "out_stateC, _ = metropolis(ini_state, beta=1, M=100000000)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10, 3))\n", "ax1, ax2, ax3 = fig.subplots(1, 3)\n", "ax1.imshow(out_stateA)\n", "ax2.imshow(out_stateB)\n", "ax3.imshow(out_stateC)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "ini_state = create_initial_state(N)\n", "\n", "beta = 0.25\n", "ini_state, _ = metropolis(ini_state, beta=beta, M=100000000)\n", "\n", "out = []\n", "for _ in range(200):\n", " ini_state, _ = metropolis(ini_state, beta=beta, M=1000000)\n", " out.append(ini_state)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from IPython.display import HTML\n", "from matplotlib.animation import FuncAnimation\n", "fig, ax = plt.subplots()\n", "\n", "def animate(i):\n", " ax.cla()\n", " ax.imshow(out[i])\n", "\n", "ani = FuncAnimation(fig, animate, frames=len(out), interval=20)\n", "\n", "#HTML(ani.to_jshtml())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "ini_state = create_initial_state(N)\n", "\n", "state, energyA = metropolis(ini_state, beta=1, M=100000000)\n", "state, energyB = metropolis(ini_state, beta=0.22, M=100000000)\n", "state, energyC = metropolis(ini_state, beta=0.1, M=100000000)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(energyA, label=r'$\\beta=1')\n", "ax.plot(energyB, label=r'$\\beta=1')\n", "ax.plot(energyC, label=r'$\\beta=1')\n", "\n", "ax.grid()\n", "\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On observe des fluctuations importantes pour la courbe $\\beta=0.2$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "Tbeta = np.logspace(-2, 0.3, 201)\n", "\n", "@jit(parallel=True)\n", "def metropolis_over_beta(Tbeta, M=200000000):\n", " Nbeta = len(Tbeta)\n", " res = np.zeros((Nbeta, 1000))\n", " for i in numba.prange(Nbeta) :\n", " beta = Tbeta[i]\n", " ini_state = 2*(np.random.rand(N, N)>.5) - 1\n", " state, output = metropolis(ini_state, beta, M)\n", " res[i,:] = output[-1000:]\n", " return res" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "res = metropolis_over_beta(Tbeta)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'T')" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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praVsOlDFXVfOY9L45EiXI3LaQgoCM8s0s9+b2b7gnxN66XOJmW3r9tNiZtcE5z1iZoe6zVsaSj0iw6WhtYOvr9vNudMncItGG5NRLtQjgruBF9x9LvBCcPpd3P0ld1/q7kuBS4Em4Hfdunzp5Hx33xZiPSLD4rFXDlPd2MY/fHSBBpqRUS/UIFgJPBr8/ChwTT/9rwd+6+5NIW5XJGIaWzt4cONBPnhGtp4ZkKgQahBMcvdjwc9lQH+3TdwEPN6j7Wtm9qaZfcfMkvpa0MxWm1mhmRVWVFSEULJIaB7ZdJiapnb++rK5kS5FJCz6DQIz22BmO3r5Wdm9n7s74KdYzxS6BrBf3635HmAe8D4gE7irr+XdfY27F7h7QXa2BvmQyDh+ooX7X9rP8vmTOHf6ey6JiYxK/T794u7L+5pnZsfNbIq7Hwt+0ZefYlU3As+4e3u3dZ88mmg1sx8DXxxg3SIR8c3n99DR6fz9R+ZHuhSRsAn11NBaYFXw8yrg2VP0vZkep4WC4YF1jdxxDbAjxHpEhszbx+v51dZSbnv/DI0/LFEl1CC4D7jczPYBy4PTmFmBmT10spOZzQCmAn/ssfzPzOwt4C0gC/jXEOsRGTIP/OEAYxPjueNivWJaoktIL0Zx9yrgsl7aC4HPdJs+DOT10u/SULYvMlyOVDWxdvtRbrtwBhNSNeqYRBc9WSwyAA/88QDxZtx+8axIlyISdgoCkX6U1bXw9JYSbijI16skJCopCET68eDLB+l05w4NPylRSkEgcgp1Te38fPMRVi7JZWrm2EiXIzIkFAQip/D01hKa2zv5y/fPjHQpIkNGQSDSB3fnZ5uLWDo1g0V56ZEuR2TIKAhE+rD5UDUHKhr5+Hl6zbRENwWBSB8ee+Uw45PH8NHFuZEuRWRIKQhEelFc3cTzO8q45bzppCTGR7ockSGlIBDpxSObDhNnxqoLp0e6FJEhpyAQ6aGhtYMnXi/mo4unMCU9JdLliAw5BYFID8+9eZSG1g5uvWBGpEsRGRYKApEefllYwqzsVM6ZlhHpUkSGhYJApJuDFQ0UFtVww7lT6RomQyT6KQhEunl6awlxBted8563potELQWBSJC789ybx7hoTpbeMioxJeQgMLMbzGynmQXMrOAU/VaY2V4z229md3drn2lmm4PtT5iZRv2QiNh9rJ7DVU1cddaUSJciMqzCcUSwA7gO2NhXBzOLB+4HrgQWADeb2YLg7G8C33H3OUAN8Okw1CQyaL/dcYw4gysWTIp0KSLDKuQgcPfd7r63n27LgP3uftDd24BfACuDg9ZfCjwV7PcoXYPYiwwrd+e5t45x/qyJTByXFOlyRIbVcF0jyAOKu02XBNsmArXu3tGjXWRY7Stv4GBFI1fqtJDEoAENXm9mG4DJvcy6192fDW9JfdawGlgNMG2a3gYp4bXurWOYwYcX6rSQxJ4BBYG7Lw9xO6XA1G7T+cG2KiDDzMYEjwpOtvdWwxpgDUBBQYGHWI/Iuzy/o4z3Tc8kJ013C0nsGa5TQ68Dc4N3CCUCNwFr3d2Bl4Drg/1WAcNyhCFy0oGKBvaU1XPlWb0d9IpEv3DcPnqtmZUAFwDPmdn6YHuuma0DCP62fyewHtgNPOnuO4OruAv4GzPbT9c1g4dDrUlkMJ7fUQbAikUKAolNAzo1dCru/gzwTC/tR4Gruk2vA9b10u8gXXcViUTEi3vKWZKfrjeNSszSk8US0xpaO9heXMtFc7IiXYpIxCgIJKa9friajoBz4WwFgcQuBYHEtFcOVJEYH8e50ydEuhSRiFEQSEzbdKCSs6dlaFxiiWkKAolZtU1t7Dx6QqeFJOYpCCRmvXqwGne4cM7ESJciElEKAolZrxyoJCUhniX5GZEuRSSiFAQSszYdqGLZzEwSx+ifgcQ2/QuQmFR+ooV95Q1cOFunhUQUBBKTXjlYBaALxSIoCCRGbdpfxfjkMSzIHR/pUkQiTkEgMWnzoa7rA/FxFulSRCJOQSAx5/iJFg5XNXHeTF0fEAEFgcSg1w5VA7BsZmaEKxEZGRQEEnNeP1zN2MR4Fur6gAigIJAY9Nqhas6dPoEx8dr9RUBBIDGmtqmNPWX1nKfTQiLvCCkIzOwGM9tpZgEzK+ijz1Qze8nMdgX7/r9u875iZqVmti34c1Vv6xAJl+0ldQCcO11BIHJSqENV7gCuA354ij4dwN+6+1YzSwO2mNnv3X1XcP533P3bIdYhMiB7y04AMG9yWoQrERk5QgoCd98NYNb3vdjufgw4Fvxcb2a7gTxgV58LiQyRvWUN5KQlMSE1MdKliIwYw3qNwMxmAGcDm7s132lmb5rZj8ysz2GizGy1mRWaWWFFRcVQlypR6u3j9ZypowGRd+k3CMxsg5nt6OVn5WA2ZGbjgKeBz7v7iWDzA8BsYCldRw3/3tfy7r7G3QvcvSA7O3swmxYBoDPgXUEwSUEg0l2/p4bcfXmoGzGzBLpC4Gfu/qtu6z7erc+DwG9C3ZZIX45UN9HaEeAMHRGIvMuQnxqyrgsIDwO73f0/esyb0m3yWrouPosMib1l9QA6IhDpIdTbR681sxLgAuA5M1sfbM81s3XBbhcBtwKX9nKb6LfM7C0zexO4BPhCKPWInMrbx7uCYO6kcRGuRGRkCfWuoWeAZ3ppPwpcFfz8J6DX24rc/dZQti8yGHvL6pmWOZaxiaHeNS0SXfRkscSMg5WNzMnR0YBITwoCiQnuTnF1E9Myx0a6FJERR0EgMaGmqZ2G1g4FgUgvFAQSE45UNwEoCER6oSCQmHAyCKYqCETeQ0EgMaH4nSBIiXAlIiOPgkBiwpGqJrLGJenWUZFeKAgkJhypbmKajgZEeqUgkJhwRLeOivRJQSBRr70zwLG6ZgWBSB8UBBL1jtY2E3DdMSTSFwWBRL1DlY2AniEQ6YuCQKLermPBcYqnjI9wJSIjk4JAot7O0hNMzUwhPSUh0qWIjEgKAol6O4/WsSg3PdJliIxYCgKJaida2jlc1cTCXJ0WEulLqCOU3WBmO80sYGYFp+h3ODgS2TYzK+zWnmlmvzezfcE/J4RSj0hPu492XR9YmKcjApG+hHpEsAO4Dtg4gL6XuPtSd+8eGHcDL7j7XOCF4LRI2Ow4GQQ6IhDpU0hB4O673X1vCKtYCTwa/PwocE0o9Yj0tPNoHTlpSeSkJUe6FJERa7iuETjwOzPbYmaru7VPcvdjwc9lwKS+VmBmq82s0MwKKyoqhrJWiSI7S0/oaECkH/2+itHMNgCTe5l1r7s/O8DtvN/dS80sB/i9me1x93edTnJ3NzPvawXuvgZYA1BQUNBnP5GTWto72V/RwBUL+/z9QkQYQBC4+/JQN+LupcE/y83sGWAZXdcVjpvZFHc/ZmZTgPJQtyVy0p6yejoDzkLdOipySkN+asjMUs0s7eRn4Aq6LjIDrAVWBT+vAgZ6hCHSrx2ldYAuFIv0J9TbR681sxLgAuA5M1sfbM81s3XBbpOAP5nZduA14Dl3fz447z7gcjPbBywPTouExc6jJ0hPSSB/gsYhEDmVkIZrcvdngGd6aT8KXBX8fBBY0sfyVcBlodQg0pedR+tYmDseM4t0KSIjmp4slqjU3hlgz7F6FulBMpF+KQgkKu0vb6CtM6DrAyIDoCCQqLT5YBUAS/IzIluIyCigIJCotH7ncebmjGNGVmqkSxEZ8RQEEnWqG9vYfKiKFYt6ew5SRHpSEEjU2bDrOAGHDy9UEIgMhIJAos76nWXkZaToQrHIACkIJKo0tHbw8r5KViyarOcHRAZIQSBR5aU95bR1BnRaSGQQFAQSVdbvLCNrXCLnTtdgdyIDpSCQqNHS3slLe8q5fMEk4uN0WkhkoBQEEjX+tK+SxrZOnRYSGSQFgUSNp7eWkJmayIWzsyJdisiooiCQqFDd2MaG3ce5ZmkeiWO0W4sMhv7FSFR4dlsp7Z3ODQX5kS5FZNRREEhUeHprCYvyxjN/ih4iExmsUEcou8HMdppZwMwK+uhzpplt6/Zzwsw+H5z3FTMr7TbvqlDqkdh0tLaZHaUn+Nji3EiXIjIqhTRCGV1jD18H/LCvDu6+F1gKYGbxQCnvHtXsO+7+7RDrkBj24p5yAC6bnxPhSkRGp1CHqtwNDOZR/suAA+5eFMp2Rbp7cU850zLHMjt7XKRLERmVhvsawU3A4z3a7jSzN83sR2amx0FlUJrbOvnz/kounZejdwuJnKZ+g8DMNpjZjl5+Vg5mQ2aWCFwN/LJb8wPAbLpOHR0D/v0Uy682s0IzK6yoqBjMpiVKuTuPv3aE1o6ATguJhKDfU0PuvjxM27oS2Orux7ut+53PZvYg8JtT1LEGWANQUFDgYapJRrG7n36LJwqLWTYjk/NmTox0OSKj1nCeGrqZHqeFzGxKt8lr6br4LNKvXUdP8ERhMZ+6cAaPrz5fD5GJhCDU20evNbMS4ALgOTNbH2zPNbN13fqlApcDv+qxim+Z2Vtm9iZwCfCFUOqR2PHTzUUkjYnj88vn6gVzIiEK9a6hZ3j3raAn248CV3WbbgTec+zu7reGsn2JTfUt7fz3G6V8bEkuGWMTI12OyKin42kZdR57pYimtk4+cf70SJciEhUUBDKq7Cit4z83vM2HF05iSX56pMsRiQoKAhk12joCfOGJbWSmJnLfdYv13IBImIT6igmRYfOTV4vYV97Aw6sKmJCqawMi4aIjAhkVahrb+O6Gt7n4jGwunaeHx0TCSUEgI97R2mY+9cjrNLZ18vcfma9TQiJhplNDMmK5O09tKeFr63bT0el8/+PncMaktEiXJRJ1FAQyIu0vb+DeZ95i86Fqzp0+gW9dv1hvFxUZIgoCGVHcnV+8Xsw/rd1J8pg4vnHdWfxFwVTi9PSwyJBREMiIsa24lu9ueJuX9lbwgblZ/MeNS8lOS4p0WSJRT0EgEefufP8PB/i39XvJGJvAPVfO4zMfmKV3CIkMEwWBRFRZXQv/+OwOfrfrOB9bkss3rjuLcUnaLUWGk/7FScSs31nGF5/cTltngC9fNY/bPzBLt4aKRICCQIZUc1snAXdSk8ZQXt/C9uI6jlQ3UXi4mt/uKGNJfjrfu/lspk9MjXSpIjFLQSBhV36ihe0ldWwrruGxTUW0BwK8b0Ymrx6sor2za3C5yeOTue2iGdy1Yh7JCfERrlgktikIpF+Fh6uZnJ5M/oSxVDW0kjAmjvHJCQD84I8H+P5L+1mcn8Fl83NISYjnq7/ZRWNbJwArFk5mQmoCG9+u5OZl01i5NI9pmWN1N5DICBJTQdDa0UlifFyv56Gb2zo5VNlIZmoik8YnYWbUNbfz9vF6KupbaW7rJHFMHIvy0pkxcey71lF+ooWAw4mWdirqW1k6NYPUbhc8txXX8uM/H+IT509ncX46v9t5nAW549/1gFQg4Pzk1SJKa5tJGhPHzKxUZmWPY2ZWKukpCe+p1935+WtH+OPeCk60tPPBM3K4emkueRkp76yvqrGtzy/cvWX17CuvZ0l+Bl9ft5sdR+tYffFsWts7aWjt4JbzppGTlszesnpu/OErJMTHccHsiby8r5LOgDMrK5W8CSm8vK+SZTMzKTvRwj//ehcABdMncM9V85k+cSxZ4/SFLzLSmXto48Cb2b8BHwPagAPAbe5e20u/FcB3gXjgIXe/L9g+E/gFXSOYbQFudfe2U22zoKDACwsLB13rV9bu5KevFpGZmshZeemkpySwcV8FJ5o7aOsMvNMvLWkMSQlxVDb0XkZeRgqXL5jEpPHJvLSnnNcOV79rfnJCHHNz0ugIOG0dnRyoaAQgId7IzUihqKoJgPlTxuPuXLFgEmUnWniysITkhDjaOgIEuv1vyRqXyILcdPIyktlaVMucnHFMTk/m4T8dYmZWKikJ8ew6dgKAJfnpjImPY395A3XN7bx/ThafXz6XJVMzeOL1Yg5UNJCWnMAP/nDgnf/mhHhjdvY49pTVA2AGifFxfPGKM/nzgUq2FtXw/rlZbD5YzbVn5zEhNZFtxbXsOnqCS+Zl889XLyI+zjhc2cjBygYunpvNmHi9xkpkpDGzLe5e8J72MATBFcCL7t5hZt8EcPe7evSJB96ma9ziEuB14GZ332VmTwK/cvdfmNkPgO3u/sCptnm6QfDS3nIKD1dTVtfK1iM11DS18cEzssnNSCElIZ6ZWalUNbRyuKqJ1o4A+RNSWJA7nsnjkxmbGE9DawfbimvZsOs4f95fRVtngNz0ZD5xwXQyUhJJTYonPSWBF/eUU1TVREJ8HIljjLk5afzF+6Zy7zNvsa+8gS9fNZ89ZfW8WVJLW0eATQeqALjzkjn87RVn0N7pHKlu4mBFA4cqGzlQ0cD24jpKa5tZMjWdbUdqaWzr5MaCfO67bjFxcUZRVSO/3n6UjfsqSYg38jJSmDw+mZ9uPkJ1YxvjksbQ0NpBYnwcbZ0BPnRmNrd/YBavHarmioWTWDBlPG8U1zJpfDLtHQG+vm43v9t1HIAvXzWP1RfPHvTft4iMLEMWBD02ci1wvbt/vEf7BcBX3P3Dwel7grPuAyqAycEgeVe/vpxuEISTu9PU1klyQvygHnxy9/ecmnrjSA1Hqpu4eknugG6frKhvpfBwNR9eOLnfVy80tHbwm+1HeXl/JVcvyeXSeTkcrW1m6oSxp1zW3fnhxoO8fqia+z9+ji7oikSB4QqCXwNPuPtPe7RfD6xw988Ep28FzgO+Arzq7nOC7VOB37r7ol7WvRpYDTBt2rRzi4qKwla3iEgs6CsIBnSx2Mw2AJN7mXWvuz8b7HMv0AH8LJRC++Lua4A10HVEMBTbEBGJRQMKAndffqr5ZvYp4KPAZd77IUYpMLXbdH6wrQrIMLMx7t7RrV1ERIZJyLd2BO8G+jvgandv6qPb68BcM5tpZonATcDaYGi8BFwf7LcKeDbUmkREZODCcY/ffwFpwO/NbFvwzh/MLNfM1gEEf9u/E1gP7AaedPedweXvAv7GzPbTdQvpw2GoSUREBijkB8pOXujtpf0ocFW36XXAul76HQSWhVqHiIicHj31IyIS4xQEIiIxTkEgIhLjwvpA2XAxswqgCEgH6ga5+GCW6a9vKPP7mpcFVA6ousg4nb/z4Vz3YNcRzv2hvz7aH4Z/3UP5HRHq/nCq+adaLpR9Yrq7Z7+n1d1H7Q+wZiiX6a9vKPP7mgcURvrvNdx/58O57sGuI5z7w+n+P9f+MHL2h8EsE+r+0M//91PtK2HfJ0b7qaFfD/Ey/fUNZf7p1D4SDGXd4Vj3YNcRzv2hvz7aH4Z/3UP5HRHq/nCq+cO6P4zKU0PRzMwKvZd3gUhs0v4gPQ3FPjHajwii0ZpIFyAjivYH6Sns+4SOCEREYpyOCEREYpyCQEQkxikIRERinIJgBDOzVDN71MweNLOP97+ERDszm2VmD5vZU5GuRSLPzK4Jfj88ERw//rQoCIaZmf3IzMrNbEeP9hVmttfM9pvZ3cHm64Cn3P124OphL1aGxWD2CXc/6O6fjkylMhwGuT/8d/D74Q7gL053mwqC4fcIsKJ7g5nFA/cDVwILgJvNbAFdI7YVB7t1DmONMrweYeD7hES/Rxj8/vD3wfmnRUEwzNx9I1Ddo3kZsD/4214b8AtgJVBCVxiA/l9FrUHuExLlBrM/WJdvAr91962nu019uYwMefzvb/7QFQB5wK+A/2NmDzB6X0Egp6fXfcLMJgZHATzbzO6JTGkSAX19R3wOWA5cb2Z3nO7KQx6hTIaOuzcCt0W6Dhk53L2KrvPBIrj794DvhboeHRGMDKXA1G7T+cE2iV3aJ6S7Id0fFAQjw+vAXDObaWaJwE3A2gjXJJGlfUK6G9L9QUEwzMzsceAV4EwzKzGzT7t7B3AnsB7YDTzp7jsjWacMH+0T0l0k9ge9dE5EJMbpiEBEJMYpCEREYpyCQEQkxikIRERinIJARCTGKQhERGKcXjEhEiIzmwi8EJycTNebYiuC08uCLwkTGbH0HIFIGJnZV4AGd/92pGsRGSidGhIRiXEKAhGRGKcgEBGJcQoCEZEYpyAQEYlxCgIRkRin20dFRGKcjghERGKcgkBEJMYpCEREYpyCQEQkxikIRERinIJARCTGKQhERGKcgkBEJMb9D2nGLNiX6u8lAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.semilogx(1/Tbeta, res[:, -100:].mean(axis=1)/(2*N**2))\n", "ax.set_xlabel('T')" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'T')" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.semilogx(1/Tbeta, res[:, -500:].std(axis=1))\n", "ax.set_xlabel('T')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "L'énergie moyenne est donnée par : \n", "\\begin{equation}\n", "\\left = -\\frac{\\partial\\ln Z}{\\partial \\beta}\n", "\\end{equation}\n", "\n", "Les fluctuations d'énergie par la dérivée seconde." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "from numpy import pi, sin, cos, cosh, sinh, log, exp, sqrt\n", "\n", "def integrande(theta, beta, J):\n", " x = 2*sinh(2*beta*J)/cosh(2*beta*J)**2\n", " return 1/(2*pi)*log((1+sqrt(1-x**2*sin(theta)**2))/2)\n", "\n", "def Log_Z(beta, J, N):\n", " Ntheta = 1000\n", " Ttheta = np.arange(Ntheta+1)*pi/Ntheta\n", " dtheta = Ttheta[1]-Ttheta[0]\n", " I = np.zeros_like(beta)\n", " for theta in Ttheta:\n", " I += integrande(theta, beta, J)*dtheta\n", " return N*(log(2*cosh(2*beta*J))+I)\n", " \n", "def mean_energy(beta, J, N):\n", " LZ = np.array(Log_Z(beta, J, N))\n", " return -(LZ[1:]-LZ[:-1])/(beta[1:]-beta[:-1])/(2*J*N), (beta[1:]+beta[:-1])/2" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#J = 1\n", "#N = 300\n", "\n", "Tbeta2 = np.logspace(-2, 0.3, 1000) \n", "\n", "analytic_energy, Tbeta_diff = mean_energy(Tbeta2, J, N)\n", "\n", "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "\n", "ax.semilogx(1/Tbeta_diff, analytic_energy, label='Analytic')\n", "ax.semilogx(1/Tbeta, res[:, -100:].mean(axis=1)/(2*J*N**2),label='Simu')\n", "ax.set_xlabel('T')\n", "ax.legend()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fluctuation_enery = (analytic_energy[1:] - analytic_energy[:-1])/(Tbeta_diff[1:] - Tbeta_diff[:-1])\n", "\n", "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "\n", "ax.semilogx(1/Tbeta_diff[1:], -fluctuation_enery, label='Analytic')\n", "ax.semilogx(1/Tbeta, res[:, -500:].var(axis=1)/(2*J*N**2),label='Simu')\n", "\n", "ax.set_xlabel('T')\n", "ax.legend()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import root" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.2203434])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def fun(beta, J):\n", " return np.sinh(2*beta*J)-1\n", " \n", "sol = root(fun, 1, args=(J,))\n", "sol.x" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "\n", "ax.semilogx(1/Tbeta_diff[1:], -fluctuation_enery, label='Analytic')\n", "plt.axvline(1/sol.x, color='k')\n", "\n", "ax.semilogx(1/Tbeta, res[:, -500:].var(axis=1)/(2*J*N**2),label='Simu')\n", "\n", "\n", "\n", "\n", "\n", "ax.set_xlabel('T')\n", "ax.legend()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }