{ "cells": [ { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import quad\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def Helmholtz_free_energy(beta):\n", " \"\"\"\n", " Argument: Inverse temperature beta=1/T\n", " Returns: Exact Helmholtz_free_energy per side\n", " https://en.wikipedia.org/wiki/Square_lattice_Ising_model\n", " https://arxiv.org/abs/cond-mat/9511003\n", " \"\"\"\n", "\n", " def f(x):\n", "\n", " k=(2*np.sinh(2*beta)/(np.cosh(2*beta)**2))\n", " return (1/(2*np.pi))*np.log(0.5*(1 +np.sqrt(1-(k**2)*np.sin(x)**2)))\n", "\n", " a=0\n", " b= np.pi\n", " \n", " result_quad, error = quad(f, a, b)\n", "\n", " return np.log(2*np.cosh(2*beta))+result_quad\n", "\n", "def U_exact(beta, J):\n", " \"\"\"\n", " Arguments: \n", " beta inverse temperature (1/T),J coupling in Ising model\n", " Returns:\n", " Internal energy per site\n", " https://en.wikipedia.org/wiki/Square_lattice_Ising_model\n", " \"\"\"\n", " def g(x):\n", " k=(1/(np.sinh(2*beta)**2))\n", " return 1/(np.sqrt(1-4*k*((1+k)**(-2))*np.sin(x)**2))\n", "\n", " a=0\n", " b= np.pi/2\n", " Integral, error=quad(g, a, b)\n", "\n", " U=-J*(np.cosh(2*beta*J)/np.sinh(2*beta*J))*(1+(2/np.pi)*(-1+2*np.tanh(2*beta*J)**2)*Integral)\n", "\n", " return U \n", "\n", "def M_exact(beta,J):\n", " \"\"\"\n", " Arguments: \n", " beta inverse temperature (1/T),J coupling in Ising model\n", " Returns:\n", " Exact solution for magnetization per side\n", " https://en.wikipedia.org/wiki/Square_lattice_Ising_model\n", " \"\"\"\n", "\n", " M=(1-np.sinh(2*beta*J)**(-4))**(1/8)\n", " return M" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T_crit=2.26918531421\n", "\n", "beta_list=np.linspace(0.1,1,20)\n", "y=[Helmholtz_free_energy(x) for x in beta_list ]\n", "\n", "plt.plot(beta_list, y,color='black', label=r'$-\\beta \\,f_{\\infty}$')\n", "\n", "# Adding a vertical line\n", "beta_c = 1/T_crit # critical beta\n", "plt.axvline(x=beta_c, color='black', linestyle='--', label=r'$\\beta_c \\,J$')\n", "\n", "# Add labels and a legend\n", "plt.xlabel(r'$\\beta J$')\n", "plt.ylabel(r'$U$')\n", "plt.title(r'Helmholtz free energy density $U$')\n", "plt.legend()\n", "\n", "plt.grid(True) " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T_crit=2.26918531421\n", "J=1\n", "N=100\n", "a=0.1\n", "b=1\n", "eps=(b-a)/N\n", "beta_list=np.linspace(0.1,1,N)\n", "y=[U_exact(x,J) for x in beta_list]\n", "\n", "plt.figure()\n", "plt.plot(beta_list, y,color='black', label=r'$U$')\n", "\n", "# Adding a vertical line\n", "beta_c = 1/T_crit # critical beta\n", "plt.axvline(x=beta_c, color='black', linestyle='--', label=r'$\\beta_c \\,J$')\n", "\n", "# Add labels and a legend\n", "plt.xlabel(r'$\\beta J$')\n", "plt.ylabel(r'$-\\beta U$')\n", "plt.title(r'Internal energy density $-\\beta \\, U$')\n", "plt.legend()\n", "\n", "plt.grid(True) \n", "\n", "plt.figure()\n", "y=-np.gradient(y,eps)\n", "plt.plot(beta_list, y,color='black', label=r'$-\\beta \\,f_{\\infty}$')\n", "\n", "# Adding a vertical line\n", "beta_c = 1/T_crit # critical beta\n", "plt.axvline(x=beta_c, color='black', linestyle='--', label=r'$\\beta_c \\,J$')\n", "\n", "# Add labels and a legend\n", "plt.xlabel(r'$\\beta J$')\n", "plt.ylabel(r'$SH$')\n", "plt.title(r'Specific heat $-\\frac{\\partial U}{\\partial \\beta} $')\n", "plt.legend()\n", "\n", "plt.grid(True) " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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ioqIKj4uKirT2FxYWau0vLCzUeiwIAoCHtwEvLCxEYWFhhZovX75ssO8vk8m0wo6Dg4P483Gbo6Oj+LP85uDgYBLDe0RExkjScJOfn49///1XfJ6amoqTJ0+iSZMmaN68OWbNmoVbt27h+++/BwBMnjwZy5Ytw4wZMzBhwgTs2bMHGzduxPbt26X6CgRALpeLPSNSEwQBKpVKDDWPbnl5eThw4AA6duwoHqdUKqFUKis8LigogFKpFH9qHmueFxUViefU7Dcke3t7ODk5wdHREU5OTuJjZ2dn8blmc3Z2Fvc3atRIfO7o6MiQRET1pqCgAA4ODgAe/o63t7eXpA5Jw82xY8fw9NNPi881c2PGjRuHNWvW4M6dO7h+/br4eosWLbB9+3a88847+Oqrr9CsWTN8++23vAycRDKZTJzr4+zsXOF1Ta+SIXq9ysrKtAJP+S0/Px8FBQXIy8sTn+fn54vP8/LyxOean5pNM8yn+aw7d+7oXaNMJhMDT3Vb48aNtbYmTZqgcePGRhFYiYh0JWm4GTBggDiEUJnK7j48YMAAnDhxog6rIqoZuVwuDiMZiiAIKCoqQl5eHnJzc8XAk5ubK26a5zk5OcjJyREfl9/34MEDqFQqCIIg7rt27ZrO9djY2Ihhp0mTJmjUqBGUSiX+/PNPuLq6wsXFRWvT7DPkFRJERLoyqTk3ROZOJpOJQ3xubm56f44mJJUPO5otJycH9+/fF5/fv3+/0k2tVov3b3q09ygpKana8zs6Oophp2nTpnB1dRUfP7q5ubnBycmpwU3KJqK6w3BDZIbKhyQPDw+d3y8IAvLy8nDv3j3cv38fd+/exf3795GVlYVDhw6hadOm4v7y271796BWq8Uep7S0tBqdz9raGm5ublqbu7u71ubh4QF3d3e4urpyHhERVYvhhogq0MzVcXJygp+fn7hfpVLB29u7yjlLarUaDx48QHZ2NrKzs3H37l1kZ2cjKytL/Pnolp+fj5KSEty8eRM3b958bG1yuRxubm5i2PH09NTavLy84OXlBQ8Pj0pvA0FE5o/hhogMxsLCQpyf07Zt2xq9p7CwEFlZWcjIyEBmZiYyMzORkZGhtWVmZiI9PR3Z2dkoKyurdKisMi4uLmLY8fb2rrA1a9YMrq6uHBIjMjMMN0QkKVtbWzRv3hzNmzd/7LEqlQpZWVlIT08XN03Q0Wy3b9/GnTt3UFJSIg6XnT59usrPVCgUaNasGZo1awYfHx80a9ZMrMfHxwfNmzeHs7MzAxBRDcjlcgwcOFB8LBWGGyIyGVZWVmJPTHUEQcC9e/fEsHPr1q0K282bN5GZmYni4mJcuXIFV65cqfLzHB0d0bx5c/j6+lbYWrRoAXd3d4YfIjy8wtIY7j3HcENEZkcmk4mXp/v7+1d5XElJCW7fvo0bN27g5s2buHHjhrhdv34dN27cQHZ2NvLy8nD27FmcPXu20s+xsbGBn5+fuLVs2VJrq+yeS0RUdxhuiKjBsra2FgNJVZRKpRh2rl27Jm5paWm4du0abt68iaKiIly4cAEXLlyo9DOaNGmCFi1awNbWFocPH0a7du3QunVrtGrVCh4eHuz1ITIwhhsiomrY2dmhXbt2aNeuXaWvq1Qq3LhxA2lpaUhLS8PVq1eRmpqKq1ev4urVq8jMzMS9e/dw7949AMCBAwe03m9vb482bdqgTZs2aNu2rfi4Xbt2cHFxqfPvR2RIBQUF4j26MjMzG+byC0REps7KykocfqpMfn4+UlNTceHCBezYsQPW1ta4evUq/v33X1y/fh0FBQU4efIkTp48WeG9Li4uaN++Pdq1ayf+7NChA1q2bCnpZE2i6iiVSqlLYLghIqpLDg4O6Ny5M9q3bw9ra2utewSVlJQgNTUVly5dwuXLl8Xt0qVLuHHjBu7evYu//voLf/31l9ZnWltbi0GnY8eO6NChAzp16oS2bdvWes00InPAcENEJBFNSKlsyKugoACXL1/GhQsXcPHiRVy8eFGc11NYWIjTp09XuMTdysoK7dq1g7+/P/z9/dGpUyd07twZLVq04F2dqUFhuCEiMkL29vbo1q0bunXrprVfrVbj2rVrOH/+PM6dO4fz58/j7NmzOHfuHPLy8nDmzBmcOXNG6z2a3qMuXbqgS5cu6Nq1Kzp37gwnJ6d6/EZE9YfhhojIhFhYWKBFixZo0aKFeLM04OG9fW7cuCGGG8127tw55Ofn49ChQzh06JDWZ7Vq1Qrdu3fHE088IW7u7u71/ZWIDI7hhojIDMhkMvHOyuVDT2lpKS5fvox//vkHp06dwqlTp/DPP//g5s2b4s0LN23aJB7v6emJnj17iluPHj0YeMjkMNwQEZkxS0tLdOjQAR06dMCIESPE/Xfv3sWJEye0tosXL+LOnTv4/fff8fvvv4vH+vj4oGfPnujVqxcCAgLQq1cvODo6SvF1yMhZWFigf//+4mOpMNwQETVALi4uCA4ORnBwsLgvPz8f//zzD1JSUnDs2DEcO3YMFy5cEO/avGXLFgAPe4k6deqEJ598EgEBAXjyySfRsWNHTlom2NraIjk5WeoyGG6IiOghBwcHBAUFISgoSNyXl5eHEydO4OjRozhy5Aj+/vtvXLt2TZzT8+233wIAnJ2dERgYiKCgIDz11FPo3bs37OzspPoq1MAx3BARUZUcHR3Rr18/9OvXT9yXnp6Ov//+G4cPH8bff/+NI0eOICcnBzt37sTOnTsBPBwOe+KJJ/DUU0+J72/SpIlUX4MaGIYbIiLSiYeHB4YMGYIhQ4YAeDhp+dSpU+INBw8cOIBbt27h6NGjOHr0KL788kvIZDJ07twZAwYMQP/+/dGvXz+4urpK/E3I0AoKCsS12tLS0rj8AhERmSZLS0t0794d3bt3x1tvvQVBEHD9+nX89ddf+PPPP7Fv3z5cuHBBvFpr6dKlAIDOnTuL83769esHBwcHib8JGUJ2drbUJTDcEBGRYclkMvj6+sLX1xejRo0C8HAoSxN0kpOTce7cOfEuy19++SUsLS0RGBgohp1evXpxKQnSG8MNERHVOQ8PDwwbNgzDhg0D8HDF6OTkZOzevRuJiYlIS0vD/v37sX//fkRHR8PZ2RkhISEYOHAgnn32WQ5hkU4YboiIqN65ublphZ2rV69i9+7d2L17N5KSknDv3j1s3rwZmzdvBgB069YNbdq0QePGjREUFMRV0alavCkBERFJrmXLlnjjjTewceNGZGZm4vDhw4iOjkavXr0gk8lw8uRJbNq0Cf3794ebmxvGjx+PLVu2oKCgQOrSyQgx3BARkVGRy+UICAhATEwMjhw5gvT0dKxevRp9+/ZF48aNce/ePaxduxYvvvgiXF1dMWTIEKxevRpZWVlSl05GgsNSRERk1Nzc3PDqq6+iSZMmCA0NxdGjR7F161Zs3boVqamp+O233/Dbb7/BwsICQUFBGDZsGF5++WV4eHhIXXqDY2FhgZ49e4qPJatDsjMTERHpyNLSEv369cPixYtx5coVnDp1Ch999BG6d+8OtVqN/fv346233oKXlxeefvppxMbGskenHtna2or3N7K1tZWsDoYbIiIySZobA3744YdISUnBtWvXsHjxYgQEBEAQBCQnJ+PNN9+Ep6cnQkND8d133+HBgwdSl031gOGGiIjMQvPmzfHOO+/g8OHDSE1NxcKFC9GjRw+UlZUhMTERr7/+Ojw8PDBixAj88ccfKC0tlbpkqiMMN0REZHb8/Pwwffp0HDt2DJcvX8Ynn3yCTp06obi4GBs2bMDAgQPRvHlzzJgxA2fPnpW6XLOhVCrh5+cHPz8/KJVKyepguCEiIrPWunVrvP/++zh9+jRSUlLw1ltvwcXFBXfu3MGiRYvg7++PXr164ZtvvkFubq7U5Zo0QRBw7do1XLt2DYIgSFYHww0RETUIMpkM3bt3x9KlS3H79m1s2bIFQ4YMgaWlJY4dO4aIiAh4eXlh8uTJ+Oeff6Qul2qB4YaIiBoca2trDB06FFu3bsXt27exZMkSdOjQAQUFBfjf//6Hbt26ISgoCD/++COKioqkLpd0xHBDREQNWtOmTTF16lScPXsWe/fuxbBhw2BpaYmDBw9izJgx8PHxwcyZM3H9+nWpS6UaYrghIiLCw2GrAQMGYMOGDbhx4wbmzZsHHx8fZGdnY+HChWjZsiXGjBmDU6dOSV0qPQbDDRER0SM8PDwwe/ZsXL16FVu3bsV//vMflJWV4ccff0TXrl3x7LPPYs+ePZJOmqWqMdwQERFVwdLSEkOGDEFSUhKOHTuG4cOHw8LCAgkJCXjmmWfQs2dPbNiwgffM+f9kMhk6duyIjh07QiaTSVYHww0REVEN9OjRA+vXr8fly5cRGRkJW1tbHD9+HCNGjEDbtm0RFxfX4EOOnZ0dzp49i7Nnz8LOzk6yOhhuiIiIdNCyZUt8/fXXuH79OmJiYuDq6orU1FRMmDAB/v7+2LBhA9RqtdRlNmgMN0RERHpwdXVFdHQ0rl27hkWLFsHFxQUXL17EiBEj0L17d/z++++ckyMRhhsiIqJasLOzw7vvvourV69i7ty5cHJywj///IP//ve/CAwMRFJSktQl1hulUolOnTqhU6dOXH6BiIjI1Dk5OWHOnDlITU3Fe++9Bzs7O/z9998IDg7GM8880yAuIRcEAefOncO5c+e4/AIREZG5aNKkCebPn48rV67g7bffhrW1Nfbs2YPu3btj6tSpePDggdQlmj2GGyIiojrg4eGBr776CpcuXcJLL72EsrIyLF26FO3atcPatWs56bgOMdwQERHVIV9fX2zevBm7du1Cu3btkJmZifHjx6Nv3744ceKE1OWZJYYbIiKiehASEoJTp07hs88+g729PQ4ePIiePXsiIiIC9+/fl7o8s8JwQ0REVE+sra0xY8YMXLhwAcOHD4darcY333yDdu3aYevWrVKXZzYYboiIiOpZs2bNsH79euzZswcdO3ZEVlYWXnjhBbz22mvIy8uTujy9yWQy+Pr6wtfXl8svEBERNURPP/00jh8/jpkzZ0Imk2H16tXo1q0bDh48KHVperGzs0NaWhrS0tK4/AIREVFDpVAosGDBAuzduxfNmzfH1atX0bdvX8yePRsqlUrq8kwSww0REZER6N+/P06dOoUxY8ZArVbjk08+QWBgIC5cuCB1aSaH4YaIiMhIODs74/vvv8fGjRvRuHFjpKSkoHv37li+fLlJrFNVWFiIXr16oVevXigsLJSsDoYbIiIiI/PKK6/g9OnTCAkJQWFhISIjIzFmzBgUFRVJXVq11Go1jh07hmPHjkl6k0KGGyIiIiPk7e2NnTt34ssvv4RcLsdPP/2EZ555BpmZmVKXZvQYboiIiIyUhYUFpk2bhp07d8LZ2RkHDx5EQEAAzp49K3VpRo3hhoiIyMgFBwfj8OHDaNWqFdLS0tCnTx8kJCRIXZbRYrghIiIyAe3bt8fff/+Nfv36ITc3FwMHDsTy5culLssoMdwQERGZCBcXFyQmJmL8+PFQq9WIjIzEW2+9hdLSUqlLMyqSh5vly5fDz88PNjY2CAgIwJEjR6o9fsmSJWjXrh1sbW3h4+ODd955x+hnjxMRERmKtbU1Vq9ejQULFgAAli1bhsGDByMnJ0fiyh5ydXWFq6urpDVIGm42bNiAqKgoREdH4/jx4+jatSvCwsKqnAkeHx+P9957D9HR0Th//jy+++47bNiwAe+//349V05ERCQdmUyGmTNn4ueff4atrS127tyJ4OBg5ObmSlqXvb09srKykJWVBXt7e8nqkDTcLF68GBMnTkR4eDg6duyI2NhY2NnZYfXq1ZUef/DgQQQFBWHUqFHw8/NDaGgoRo4c+djeHiIiInP04osvYv/+/XB1dcWxY8cwZMgQSW+eZywspTpxSUkJUlJSMGvWLHGfhYUFgoODcejQoUrf06dPH/z44484cuQIevfujatXr2LHjh0YM2ZMlecpLi5GcXGx+FyTalUqlcmu2aGp21TrlxLbrnbYfvpj29UO269qXbp0wbZt2xASEoLk5GS88sor2LhxI6ysrACYT9vpUr9MkOh+zrdv34a3tzcOHjyIwMBAcf+MGTOwb98+/P3335W+b+nSpXj33XchCAJKS0sxefJkrFixosrzxMTEYO7cuRX2x8fHS7piKRERkSGdPXsWc+fORUlJCfr164dp06bBwqJ+B2iKi4vx0UcfAQDmzJkDhUJhsM9WKpUYNWoUcnJy4OTkVO2xJhVukpOTMWLECHz88ccICAjAv//+i6lTp2LixIn48MMPKz1PZT03Pj4+yM7OfmzjGCuVSoXExESEhISIyZxqhm1XO2w//bHtaoftVzM7duzAyy+/jNLSUkyaNAlLly5FaWlpvbVdQUEBGjduDAC4f/++Qefd5ObmwtXVtUbhRrJhKVdXV8jlcmRkZGjtz8jIgIeHR6Xv+fDDDzFmzBi8/vrrAIDOnTujoKAAb7zxBj744INKE6pCoag0OVpZWZn8PxBz+A5SYdvVDttPf2y72mH7VW/IkCH44YcfMGrUKPzvf/+Di4sLYmJiANRP25X/fEOfT5fPkmxCsbW1NXr06IGkpCRxn1qtRlJSklZPTnlKpbJCgJHL5QBgEqulEhER1bURI0aI0zU+/fRTfPHFFxJXVP8kvVoqKioKq1atwtq1a3H+/Hm8+eabKCgoQHh4OABg7NixWhOOBw8ejBUrVmD9+vVITU1FYmIiPvzwQwwePFgMOURERA3dpEmT8NlnnwEAZs2ahV27dklcUf2SbFgKAIYPH46srCzMmTMH6enp6NatG3bu3Al3d3cAwPXr17V6ambPng2ZTIbZs2fj1q1baNq0KQYPHoxPPvlEqq9ARERklGbMmIH79+9jwYIFWLFiBfr06YPRo0dLXVa9kDTcAEBkZCQiIyMrfS05OVnruaWlJaKjoxEdHV0PlREREZm2Tz/9FPfu3cPKlSsxfvx4tG7dGgEBAVKXVeckX36BiIiI6oZMJsPSpUsRGBiI0tJSjB07Fkqlsk7PaWdnJ/mtVhhuiIiIzJiFhQUiIiLg5eWFS5cuac1lNTR7e3sUFBSgoKCg4S6/QERERHXPwcEBK1euBPDwZrjlr1Q2Rww3REREDUBoaCgmT54MAAgPDzeaVcTrAsMNERFRA7Fo0SK0atUKN27cwLRp0wz++UVFRRg0aBAGDRqEoqIig39+TTHcEBERNRAODg5Yu3YtZDIZ1qxZg19//dWgn19WVoYdO3Zgx44dKCsrM+hn64LhhoiIqAEJCgrC9OnTAQBvvPEGsrKyJK7I8BhuiIiIGpiPPvoI/v7+yMzMxKRJk8xuCSOGGyIiogZGoVDghx9+gJWVFbZs2YIff/xR6pIMiuGGiIioAerWrZu4Yvhbb72FGzduSFuQATHcEBERNVAzZszAk08+iZycHEyYMAFqtVrqkgyC4YaIiKiBsrS0xNq1a2Fra4vdu3djxYoVUpdkEAw3REREDVjbtm2xcOFCAMAHH3yA/Px8vT/L3t4egiBAEAQuv0BERETSmTJlCtq0aYOcnByzmFzMcENERNTAaRbXBIBly5aZ/KXhDDdERESE8ePHw97eHmfPnkVycrJen1FUVIRXXnkFr7zyCpdfICIiImk5Oztj7NixAB723uijrKwMmzdvxubNm7n8AhEREUkvMjISALB161Zcv35d4mr0x3BDREREAICOHTviP//5D9RqNWJjY6UuR28MN0RERCR66623AACrVq2SdN5MbTDcEBERkej5559H8+bNkZ2djQ0bNkhdjl4YboiIiEhkaWmJN998EwDw9ddfm+Rl4Qw3REREpOX111+HQqFASkoK/v77b6nL0RnDDREREWlxdXXFyJEjAeh2WbidnR3y8/ORn58POzu7uirvsRhuiIiIqALNxOKNGzciPT29Ru+RyWSwt7eHvb09ZDJZXZZXLYYbIiIiqqB79+4IDAyESqXCqlWrpC5HJww3REREVClN701sbCxUKtVjjy8uLsb48eMxfvx4FBcX13V5VWK4ISIiokq99NJLcHd3x+3bt7Fly5bHHl9aWoq1a9di7dq1KC0trYcKK8dwQ0RERJWytrbGpEmTADy8LNxUMNwQERFRlSZNmgRLS0scOHAAJ0+elLqcGmG4ISIioip5eXnhpZdeAqD/auH1jeGGiIiIqqWZWPzTTz/h3r17ElfzeAw3REREVK0+ffqgW7duKCoqwnfffSd1OY/FcENERETVkslkeOONNwAAO3bskLiax7OUugAiIiIyfr6+vgCAvLy8Ko+xs7NDZmam+FgqDDdERET0WJqwolQqqzxGJpOhadOm9VVSlTgsRURERI9lb28PoPpwYywYboiIiOixND03BQUFVR5TXFyMiIgIREREcPkFIiIiMm41GZYqLS3FN998g2+++YbLLxAREZFxKx9uBEGQuJrqMdwQERHRY5W/+qmoqEjCSh6P4YaIiIgeq3y4MfZJxQw3RERE9FhyuRwKhQJA9ZOKjQHDDREREdVITSYVGwOGGyIiIqoRUwk3vEMxERER1cjjwo2trS1SU1PFx1JhuCEiIqIaeVy4sbCwgJ+fXz1WVDkOSxEREVGNaJZg4IRiIiIiMguP67kpKSnB9OnTMX36dJSUlNRnaVoYboiIiKhGHhduVCoVPv/8c3z++edQqVT1WZoWhhsiIiKqEVO5WorhhoiIiGqE4YaIiIjMCicUExERkVlhzw0RERGZFYYbIiIiMiumEm54h2IiIiKqkZosv3DmzBnxsVQYboiIiKhGHjeh2MLCAp06darPkiqvQ+oCiIiIyDSYyrCU5OFm+fLl8PPzg42NDQICAnDkyJFqj3/w4AEiIiLg6ekJhUKBtm3bYseOHfVULRERUcNVk+UXYmJiEBMTI+nyC5IOS23YsAFRUVGIjY1FQEAAlixZgrCwMFy8eBFubm4Vji8pKUFISAjc3NywefNmeHt749q1a2jUqFH9F09ERNTA1GT5hblz5wIApk+fDmtr63qrrTxJw83ixYsxceJEhIeHAwBiY2Oxfft2rF69Gu+9916F41evXo179+7h4MGDsLKyAgCjWFqdiIioIeCw1GOUlJQgJSUFwcHB/1eMhQWCg4Nx6NChSt/z22+/ITAwEBEREXB3d4e/vz8+/fRTlJWV1VfZREREDZap3KFYsp6b7OxslJWVwd3dXWu/u7s7Lly4UOl7rl69ij179mD06NHYsWMH/v33X0yZMgUqlQrR0dGVvqe4uBjFxcXi89zcXAAPu86kXLG0NjR1m2r9UmLb1Q7bT39su9ph++nPkG2nGTVRKpWVfl75fYb+PavLZ5nUpeBqtRpubm5YuXIl5HI5evTogVu3bmHRokVVhpv58+eL43/l7dq1S+xeM1WJiYlSl2Cy2Ha1w/bTH9uudth++jNE292/fx/Aw3Czfft2yGQyrdeLiorExwkJCbCxsan1OTV0GQqTLNy4urpCLpcjIyNDa39GRgY8PDwqfY+npyesrKwgl8vFfR06dEB6ejpKSkoqnbg0a9YsREVFic9zc3Ph4+OD0NBQODk5Gejb1C+VSoXExESEhISIKZpqhm1XO2w//bHtaoftpz9Dtp1m9EMQBDzzzDMVwkv54aqwsDBxGMsQNOeuCcnCjbW1NXr06IGkpCQMHToUwMOemaSkJERGRlb6nqCgIMTHx0OtVsPC4uF0oUuXLsHT07PKGdkKhQIKhaLCfisrK5P/B2IO30EqbLvaYfvpj21XO2w//Rmi7ZydncXHKpUKjo6OFc5hyPNV9dmPI+l9bqKiorBq1SqsXbsW58+fx5tvvomCggLx6qmxY8di1qxZ4vFvvvkm7t27h6lTp+LSpUvYvn07Pv30U0REREj1FYiIiBoMS0tLsTOhsknFNjY2OHLkCI4cOWLQISldSTrnZvjw4cjKysKcOXOQnp6Obt26YefOneIk4+vXr4s9NADg4+ODhIQEvPPOO+jSpQu8vb0xdepUzJw5U6qvQERE1KDY2dmhpKSk0jkwcrkcvXr1kqAqbZJPKI6MjKxyGCo5ObnCvsDAQBw+fLiOqyIiIqLK2NnZ4cGDB0Z9rxvJww0RERGZjupu5FdSUoKvvvoKADB16tSGeYdiIiIiMi3VhRuVSoUZM2YAAKZMmSJZuJF84UwiIiIyHaZwl2KGGyIiIqoxU1hfiuGGiIiIaozhhoiIiMwKww0RERGZFYYbIiIiMiuaCcXGHG54KTgRERHVmKbnpqrlF/bu3Ss+lgrDDREREdVYdcNScrkcAwYMqOeKKqpVuFGpVEhPT4dSqUTTpk3RpEkTQ9VFRERERsgs59zk5eVhxYoV6N+/P5ycnODn54cOHTqgadOm8PX1xcSJE3H06NG6qJWIiIgk9rg7FC9fvhzLly+HSqWq79JEOoWbxYsXw8/PD3FxcQgODsbWrVtx8uRJXLp0CYcOHUJ0dDRKS0sRGhqKZ599FpcvX66ruomIiEgCj1tbSrMgdklJSX2XJtJpWOro0aP4888/0alTp0pf7927NyZMmIDY2FjExcVh//79aNOmjUEKJSIiIumZwvILOoWbdevW1eg4hUKByZMn61UQERERGS+znHMjl8uRmZlZF7UQERGRkTPLcCMIQl3UQURERCbALMMNERERNVymEG70us/Nt99+CwcHh2qPefvtt/UqiIiIiIyX2U0o1oiNjYVcLq/ydZlMxnBDRERkhsr33AiCAJlMJr6mUCiwbds28bFU9Ao3x44dg5ubm6FrISIiIiOnCTdqtRolJSVaIcbS0hKDBg2SqjSRznNuyic0IiIialg04QYw3nk3vFqKiIiIaszKygqWlg8Hfh4NNyqVCmvWrMGaNWtMZ/kFAIiOjn7sZGIiIiIyX1VNKi4pKUF4eDjCw8MlXX5Bp3Bz/fp1REdHa3VJVefWrVt6FUVERETGy9gvB9cp3PTq1QuTJ0+udtXvnJwcrFq1Cv7+/vj5559rXSAREREZF2MPNzpdLXXu3Dl88sknCAkJgY2NDXr06AEvLy/Y2Njg/v37OHfuHM6ePYvu3btj4cKFGDhwYF3VTURERBIx9nCjU8+Ni4sLFi9ejDt37mDZsmVo06YNsrOzcfnyZQDA6NGjkZKSgkOHDjHYEBERmSljDzd63efG1tYWL7/8Ml5++WVD10NERERGztjvUqxzuJkwYUKNjlu9erXOxRAREZHxM7uemzVr1sDX1xdPPPEE73lDRETUAFUVbhQKBTZu3Cg+lorO4ebNN9/EunXrkJqaivDwcLz66qto0qRJXdRGRERERqiqcGNpaYlXXnlFipK06HwTv+XLl+POnTuYMWMGfv/9d/j4+GDYsGFISEhgTw4REVEDYOzDUjqHG+BhV9PIkSORmJiIc+fOoVOnTpgyZQr8/PyQn59v6BqJiIjIiFQ1obi0tBSbNm3Cpk2bUFpaKkVpAPS8Wqo8CwsLyGQyCIKAsrIyQ9RERERERqyqnpvi4mIMGzYMAJCfny+uQVXf9Oq5KS4uxrp16xASEoK2bdvi9OnTWLZsGa5fv851p4iIiMycsQ9L6RyppkyZgvXr18PHxwcTJkzAunXr4OrqWhe1ERERkREyu3ATGxuL5s2bo2XLlti3bx/27dtX6XG//PJLrYsjIiIi42N24Wbs2LGQyWR1UQsRERGZALO7Q/GaNWvqoAwiIiIyFcbec6PXhGIiIiJquIw93EhzjRYRERGZrKrCjbW1NeLi4sTHUmG4ISIiIp1UFW6srKwwfvx4CSrSxmEpIiIi0onZTSgmIiKihq18z40gCOJV1KWlpUhISAAAhIWFSXaHYoYbIiIi0okm3JSVlUGlUonza4qLi/H8888DMMHlF4iIiKjh0oQbwDivmGK4ISIiIp1YWVlBLpcDYLghIiIiMyCTyYx6UjHDDREREenMmG/kx3BDREREOmO4ISIiIrNizOGGl4ITERGRzioLN9bW1li2bJn4WCoMN0RERKQzzYTi8uHGysoKERERUpUk4rAUERER6UzTc2OMV0ux54aIiIh0VtmwVFlZGfbv3w8A6Nu3r3gvnPrGcENEREQ6qyzcFBUV4emnnwbwcPkFzdBVfeOwFBEREenMmK+WYrghIiIinTHcPMby5cvh5+cHGxsbBAQE4MiRIzV63/r16yGTyTB06NC6LZCIiIi0cPmFamzYsAFRUVGIjo7G8ePH0bVrV4SFhSEzM7Pa96WlpeHdd99F375966lSIiIi0mDPTTUWL16MiRMnIjw8HB07dkRsbCzs7OywevXqKt9TVlaG0aNHY+7cuWjZsmU9VktEREQAw02VSkpKkJKSguDgYHGfhYUFgoODcejQoSrf99FHH8HNzQ2vvfZafZRJREREjzDmcCPppeDZ2dkoKyuDu7u71n53d3dcuHCh0vccOHAA3333HU6ePFmjcxQXF6O4uFh8npubCwBQqVRQqVT6FS4xTd2mWr+U2Ha1w/bTH9uudth++qurttMsr1BQUKD12fPnz69wbkPQ5bNM6j43eXl5GDNmDFatWgVXV9cavWf+/PmYO3duhf27du0SU6epSkxMlLoEk8W2qx22n/7YdrXD9tOfodtO0wlx69Yt7NixQ9zfoUMHAMDu3bsNej5deogkDTeurq6Qy+XIyMjQ2p+RkQEPD48Kx1+5cgVpaWkYPHiwuE+tVgMALC0tcfHiRbRq1UrrPbNmzUJUVJT4PDc3Fz4+PggNDYWTk5Mhv069UalUSExMREhICKysrKQux6Sw7WqH7ac/tl3tsP30V1dtp1AoADzswRk4cKDBPrcqmpGXmpA03FhbW6NHjx5ISkoSL+dWq9VISkpCZGRkhePbt2+P06dPa+2bPXs28vLy8NVXX8HHx6fCexQKhfgHUJ6VlZXJ/wMxh+8gFbZd7bD99Me2qx22n/4M3XaaDoLCwkLxc8vKynD8+HEAQPfu3Q26/IIutUs+LBUVFYVx48ahZ8+e6N27N5YsWYKCggKEh4cDAMaOHQtvb2/Mnz8fNjY28Pf313p/o0aNAKDCfiIiIqo7VS2/0Lt3bwDSLr8gebgZPnw4srKyMGfOHKSnp6Nbt27YuXOnOMn4+vXrsLCQ/Ip1IiIiKodXSz1GZGRkpcNQAJCcnFzte9esWWP4goiIiKhavEMxERERmRVNz01paanRXaLPcENEREQ6K387FWMbmmK4ISIiIp1ZW1uLc2IZboiIiMjkyWQyo51UbBQTiomIiMj02NvbIz8/X5xUbGVlhejoaPGxVBhuiIiISC+P9txYW1sjJiZGwooe4rAUERER6YXDUkRERGRWHg03arUa58+fB/BwAU2pbsLLcENERER6eTTcFBYWisshSbn8AoeliIiISC/GepdihhsiIiLSi7HOuWG4ISIiIr0w3BAREZFZYbghIiIis8JwQ0RERGbFWCcU81JwIiIi0sujPTdWVlZ49913xcdSYbghIiIivVS2/MKiRYukLAkAh6WIiIhIT8Y654Y9N0RERKSXypZfuH79OgCgefPmXH6BiIiITMujE4oLCwvRokULAFx+gYiIiEyQsQ5LMdwQERGRXhhuiIiIyKww3BAREZFZYbghIiIis2KsdyhmuCEiIiK9aHpuVCoVVCqVxNX8H14KTkRERHrRhBvg4WXgCoUCU6ZMAQBYWkoXMRhuiIiISC8KhQIymQyCIECpVMLJyQnLly+XuiwOSxEREZF+ZDKZUU4qZrghIiIivZUPN4IgICsrC1lZWRAEQbKaGG6IiIhIb+WvmFIqlXBzc4Obm5ukPTkMN0RERKQ3DksRERGRWWG4ISIiIrPCcENERERmheGGiIiIzIoxLsHAcENERER6M8aeG96hmIiIiPRWPtxYWlpi3LhxALj8AhEREZmo8uFGoVBgzZo10hYEDksRERFRLXBYioiIiMxK+QnFmgU0gYehRyaTSVITe26IiIhIb+V7bpRKJRwcHODg4MDlF4iIiMg0GeOwFMMNERER6Y3hhoiIiMwKww0RERGZFd6hmIiIiMwKe26IiIjIrBhjuOF9boiIiEhv5cONXC7Hyy+/DACQy+WS1cRwQ0RERHorH25sbGywadMmiSvisBQRERHVgmZCcXFxMcrKyiSu5iGGGyIiItKbpucGMJ55Nww3REREpDcbGxvxcVZWFmQyGWQymaSXhjPcEBERkd5kMpnYe1NYWChxNQ8x3BAREVGtGNvl4Aw3REREVCuaScUMN0RERGQW2HNDREREZoVzboiIiMisGFvPDe9QTERERLWiCTdFRUUYOHAgAGmXXzCKnpvly5fDz88PNjY2CAgIwJEjR6o8dtWqVejbty8aN26Mxo0bIzg4uNrjiYiIqG5pJhSrVCps374d27dv17r/TX2TPNxs2LABUVFRiI6OxvHjx9G1a1eEhYUhMzOz0uOTk5MxcuRI7N27F4cOHYKPjw9CQ0Nx69ateq6ciIiIAOMblpI83CxevBgTJ05EeHg4OnbsiNjYWNjZ2WH16tWVHv/TTz9hypQp6NatG9q3b49vv/0WarUaSUlJ9Vw5ERERAcYXbiSdc1NSUoKUlBTMmjVL3GdhYYHg4GAcOnSoRp+hVCqhUqnQpEmTSl8vLi5GcXGx+Dw3NxfAw64zlUpVi+qlo6nbVOuXEtuudth++mPb1Q7bT3/10XaaIai7d++KQ1S3bt0SHxuCLvVLGm6ys7NRVlYGd3d3rf3u7u64cOFCjT5j5syZ8PLyQnBwcKWvz58/H3Pnzq2wf9euXVqLfZmixMREqUswWWy72mH76Y9tVztsP/3VZdvdvn0bAHDx4kWx9yYhIcGg82506RUy6aulFixYgPXr1yM5ObnKBpw1axaioqLE57m5ueI8HScnp/oq1aBUKhUSExMREhICKysrqcsxKWy72mH76Y9tVztsP/3VR9udOnUKmzdvhqurq7gvLCzMoD03mpGXmpA03Li6ukIulyMjI0Nrf0ZGBjw8PKp97+eff44FCxZg9+7d6NKlS5XHKRQKKBSKCvutrKxM/h+IOXwHqbDtaoftpz+2Xe2w/fRXl23n6OgIAFrTQAx9Pl0+S9IJxdbW1ujRo4fWZGDN5ODAwMAq37dw4ULMmzcPO3fuRM+ePeujVCIiIqoCJxQ/IioqCuPGjUPPnj3Ru3dvLFmyBAUFBQgPDwcAjB07Ft7e3pg/fz4A4LPPPsOcOXMQHx8PPz8/pKenAwAcHBzg4OAg2fcgIiJqqIxt+QXJw83w4cORlZWFOXPmID09Hd26dcPOnTvFScbXr1+HhcX/dTCtWLECJSUlePnll7U+Jzo6GjExMfVZOhEREYE9N5WKjIxEZGRkpa8lJydrPU9LS6v7goiIiKjGyoeb/v37A4BWx0R9M4pwQ0RERKZLc1VUUVFRhU4JKUh+h2IiIiIybcY2LMVwQ0RERLXCcENERERmRRNuCgoK0LRpUzRt2hQFBQWS1cM5N0RERFQrmnDz6HqOUmHPDREREdWKIZdZMASGGyIiIqoVQy6QaQgMN0RERFQrFhYWsLW1lboMEcMNERER1Zpm3o0x4ITiKpSVlUGlUkldRqVUKhUsLS1RVFSEsrIyqcsxKY9rOysrK8jlcgkqIyIybXZ2drh7967UZQBguKlAEASkp6fjwYMHUpdSJUEQ4OHhgRs3bkAmk0ldjkmpSds1atQIHh4ebFsiIh1oJhW3a9cOjo6OXH7BmGiCjZubG+zs7IzyF5xarUZ+fj4cHBwk/ctjiqprO0EQoFQqkZmZCQDw9PSUokQiIpOkGZb68ssv8dxzz0laC8NNOWVlZWKwcXFxkbqcKqnVapSUlMDGxobhRkePazvNhLjMzEy4ublxiIqIqIaM6S7F/M1YjmaOjTFNiqL6p/nzN9Y5V0RExojhxsgZ41AU1R/++RMR6U4TbqZNmwY/Pz9JQw6HpYiIiKjWNBOK7927h3v37kEQBMlqYc8NERER1ZoxTelguGmg7t69Czc3N6SlpdX4PSNGjMAXX3xRd0UREZHJYrghgxs/fjxkMhkmT55c4bWIiAjIZDKMHz9e3PfJJ59gyJAh8PPzQ0xMDGQyWbUbAMyePRuffPIJcnJy6utrERGRiWC4oTrh4+OD9evXo7CwUNxXVFSE+Ph4NG/eXNynVCrx3Xff4bXXXgMAvPvuu7hz5464NWvWDB999JHWPgDw9/dHq1at8OOPP9bvFyMiIqNnTOGGE4ofQ3NjNynoehPB7t2748qVK/jll18wevRoAMAvv/yC5s2bo0WLFuJxO3bsgEKhwJNPPgkAcHBwgIODg/i6XC6Ho6MjPDw8Kpxj8ODBWL9+PSIiIvT9WkREZIY0E4qNAcPNYyiVSq1f/PUpPz9f578sEyZMQFxcnBhuVq9ejfDwcCQnJ4vH7N+/Hz169NCrpt69e+OTTz5BcXExFAqFXp9BRETmR9Nz4+joCB8fH0lvq8FhKTPz6quv4sCBA7h27RquXbuGv/76C6+++qrWMdeuXYOXl5den+/l5YWSkhKkp6cbolwiIjITmnATGBiIs2fPSjpMxZ6bx7Czs0N+fr5k59ZV06ZNMWjQIKxZswaCIGDQoEFwdXXVOqawsBA2NjZ61aRZnsAY7kBJRETGw5juUMxw8xgymcyoxhFrYsKECYiMjAQALF++vMLrrq6uuH//vl6ffe/ePQAPQxQREZGGMYUbDkuZoWeffRYlJSVQqVQICwur8PoTTzyBc+fO6fXZZ86cQbNmzSr0BhERUcOm6Qg4c+YMOnXqJGnIYbgxQ3K5HOfPn8e5c+cqXdU6LCwMZ8+e1av3Zv/+/QgNDTVEmUREZEY0PTclJSU4d+4cl18gw3NycoKTk1Olr3Xu3Bndu3fHxo0bdfrMoqIibN26FRMnTjREiUREZEZ4nxsyuDVr1lT7+tatW7Wez5kzB9OnT8fEiRNhYaGdcatakiEuLg69e/cW749DRESkwXBDkhs0aBAuX76MW7duwcfHp0bvsbKywtdff13HlRERkSliuCGjMG3aNJ2Of/311+umECIiMnnGdGUx59wQERFRrWnug2YMGG6IiIio1iwsLMRleby9vbn8AhEREZk+zdBUYmKipHNwGG6IiIjIIIzlLsUMN0RERGQQmp6bgoICSetguCEiIiKD0CzK/Prrr6OwsFCyOhhuiIiIyCA0V0xdvnwZarVasjoYbsxEQkICZDJZtduuXbvq7Pzz589Hr1694OjoCDc3NwwdOhQXL16s9fG3bt3Cq6++ChcXF9ja2qJz5844duyY+HpeXh6mTZsGX19f2Nraok+fPjh69GiV53nhhRdw+fJlw355IiICYDw38mO4MRP9+vXDnTt3xM3FxQUffvih1r5nnnmmzs6/b98+RERE4PDhw0hMTIRKpUJoaGiV4641Of7+/fsICgqClZUV/vjjD5w7dw5ffPEFGjduLB7z+uuvIzExET/88ANOnz6N0NBQBAcH49atW1We58UXX5R8PJiIyBwZy71ueIdiM2Frayv+pbp16xbu3r2Lvn37wsPDw6DnEQSh0nsX7Ny5U+v5mjVr4ObmhpSUFPTr10+v4z/77DP4+PggLi5OPK5Fixbi48LCQvz888/49ddfxffExMTg999/x4oVK/Dxxx9XOE9cXBw8PDyQkpKCAQMG6PbliYioWsZyl2L23JihEydOAAC6d++u0/tyc3Mxc+ZMdO3aFa1bt8bEiROxZ88eKJVKXLlyBePHj8elS5dq9Fk5OTkAgCZNmuh9/G+//YaePXvilVdegZubG5544gmsWrVKfL20tBRlZWXiBDYNW1tbHDhwwCB1ERFRzbHnxsRUN4whl8u1fsFWd6yFhYXWH35Vx9Ym/R4/fhw+Pj5wcXHR6X2fffYZsrKysGjRIiiVSmzfvh0vv/wy7t+/D3t7e0yaNAl+fn6P/Ry1Wo1p06YhKCgI/v7+eh9/9epVrFixAlFRUXj//fdx9OhRvP3227C2tsa4cePg6OiIwMBAzJs3Dx06dIC7uzvWrVuHQ4cOoXXr1pWe55133kFAQECN6iIiIt0Yy5wbhpsacnBwqPK1gQMHYvv27eJzNze3Km9g1L9/fyQnJ4vP/fz8kJ2dXeE4QRD0rvX48eM699oAwLvvvovGjRvj5s2bUKvVGDp0KGJjY5GRkQEPDw+UlJRApVKJt9euSkREBM6cOVNl70lNj1er1ejZsyc+/fRTAMATTzyBM2fOIDY2FuPGjQMA/PDDD5gwYQK8vb0hl8vRvXt3jBw5EikpKZWe5+zZs1p/VkREZDia/3mXugeHw1JmqKpwc+3aNQwePBhPPPEE/P39cf36da3X7927h/79+8PHxwe+vr7w9/fH119/jaysLPzxxx/o06cPbt68We25IyMjsW3bNuzduxfNmjV7bK3VHe/p6YmOHTtq7evQoYNW3a1atcK+ffuQn5+PGzdu4MiRI1CpVGjZsmWl50lKSoK3t/dj6yIiIt01atQIADBmzBhJ59+w56aG8vPzq3xNLpdrPc/MzKzyWAsL7TyZlpZWq7oelZ2djRs3blQINyUlJRg4cCCWL1+OAQMG4P79+xV6o3766Sc8++yziIuLQ0FBAbZt24bvv/8e77//Plq3bo3Jkyejbdu2lZ5XEAS89dZb2LJlC5KTk7Um/up7fFBQUIXLwy9dugRfX98Kx9rb28Pe3h73799HQkICFi5cWOV5cnNzq62NiIj0oxmWkvqKVIabGtIlgdbVsTVx/PhxABUnE2/ZsgVPPvmkeIVQ+cupNd5//31YWv7fX4nOnTtj1qxZNTpvREQE4uPj8euvv8LR0RHp6ekAAGdnZ7F7ctmyZdiyZQuSkpJqdPw777yDPn364NNPP8WwYcNw5MgRrFy5EitXrhTPm5CQAEEQ0K5dO/z777+YPn062rdvj/Dw8CrrysvLg5WVldHM6iciMhea/65ybSkyqBMnTsDd3R1eXl5a+0+fPo3evXtX+97ywUZXK1asQE5ODgYMGABPT09x27Bhg3hMdnY2rly5UuPje/XqhS1btmDdunXw9/fHvHnzsGTJEowePVo8JicnBxEREWjfvj3Gjh2Lp556CgkJCbCysqr0PN7e3mjfvr3WeYiIyDA0v0eSk5MlXX6BPTdmZubMmZg5c2aF/e7u7jhz5gwAoKysDDk5OQa9HLomE6BjYmIQExNT4+MB4Pnnn8fzzz9f5evDhg3DsGHDalyXWq1Gbm4unJycanR+IiKqOc2Vw/fv3+fyC1T3xo8fjytXrsDf3x89e/as8f1qiIiIaoqXglO9cnR0xI4dO6Qug4iIzFhoaKjUJQBgzw0REREZSGXL80iB4YaIiIjMCsMNERERmRXOuSEiIiKDMYZJxQw3REREZBD29vaS350Y4LBUpWqzaCWZPv75ExGZNoabcjR3tZX6ttEkLc2fv+bvAxERmRYOS5Ujl8vRqFEjceFLOzs7o7msrTy1Wo2SkhIUFRVVWIiTqldd2wmCAKVSiczMTDRq1KjCgqhERFS9oqIivPTSSwCAn3/+WbxjcX0zinCzfPlyLFq0COnp6ejatSu+/vrratdB2rRpEz788EOkpaWhTZs2+OyzzzBw4ECD1OLh4QGg+pW9pSYIAgoLC2Fra2uU4cuY1aTtGjVqJP49ICKimisrKxNvGFtWViZZHZKHmw0bNiAqKgqxsbEICAjAkiVLEBYWhosXL8LNza3C8QcPHsTIkSMxf/58PP/884iPj8fQoUNx/Phx+Pv717oemUwGT09PuLm5QaVS1frz6oJKpcKff/6Jfv36cehER49rOysrK/bYEBGZOMnDzeLFizFx4kSEh4cDAGJjY7F9+3asXr0a7733XoXjv/rqKzz77LOYPn06AGDevHlITEzEsmXLEBsba7C65HK50f6Sk8vlKC0thY2NDcONjth2RETmT9JwU1JSgpSUFMyaNUvcZ2FhgeDgYBw6dKjS9xw6dAhRUVFa+8LCwrB169ZKjy8uLkZxcbH4PDc3F8DD/4M31p6Zx9HUbar1S4ltVztsP/2x7WqH7ae/+my78ucw9O9ZXT5L0nCTnZ2NsrIyuLu7a+13d3fHhQsXKn1Penp6pcenp6dXevz8+fMxd+7cCvt37dplFDcaqo3ExESpSzBZbLvaYfvpj21XO2w//dVH2xUVFYmPExISDDqhWJcrmSUflqprs2bN0urpyc3NhY+PD0JDQ+Hk5CRhZfpTqVRITExESEgIh1Z0xLarHbaf/th2tcP20199tl35G/iFhYXB3t7eYJ+tGXmpCUnDjaurK+RyOTIyMrT2Z2RkVHm1ioeHh07HKxQKKBQK8bnmBm2FhYUm+w9EpVJBqVSisLAQpaWlUpdjUth2tcP20x/brnbYfvqrz7YrLCzUemzI25VoPrsmN1qVNNxYW1ujR48eSEpKwtChQwE8vA9JUlISIiMjK31PYGAgkpKSMG3aNHFfYmIiAgMDa3TOvLw8AICPj0+taiciIqKqeXl51cnn5uXlwdnZudpjJB+WioqKwrhx49CzZ0/07t0bS5YsQUFBgXj11NixY+Ht7Y358+cDAKZOnYr+/fvjiy++wKBBg7B+/XocO3YMK1eurNH5vLy8cOPGDTg6OprsPWI0Q2s3btww2aE1qbDtaoftpz+2Xe2w/fRnLm0nCALy8vJqFJokDzfDhw9HVlYW5syZg/T0dHTr1g07d+4UJw1fv35dq1urT58+iI+Px+zZs/H++++jTZs22Lp1a43vcWNhYYFmzZrVyXepb05OTib9F1VKbLvaYfvpj21XO2w//ZlD2z2ux0ZDJnCVQJOTm5sLZ2dn5OTkmPxf1PrGtqsdtp/+2Ha1w/bTX0NsOy5MRERERGaF4cYEKRQKREdHa10FRjXDtqsdtp/+2Ha1w/bTX0NsOw5LERERkVlhzw0RERGZFYYbIiIiMisMN0RERGRWGG6IiIjIrDDcGJk///wTgwcPhpeXF2QyGbZu3Vrt8b/88gtCQkLQtGlTODk5ITAwEAkJCfVTrBHStf3K++uvv2BpaYlu3brVWX3GTJ+2Ky4uxgcffABfX18oFAr4+flh9erVdV+sEdKn/X766Sd07doVdnZ28PT0xIQJE3D37t26L9bIzJ8/H7169YKjoyPc3NwwdOhQXLx48bHv27RpE9q3bw8bGxt07twZO3bsqIdqjYs+bbdq1Sr07dsXjRs3RuPGjREcHIwjR47UU8X1g+HGyBQUFKBr165Yvnx5jY7/888/ERISgh07diAlJQVPP/00Bg8ejBMnTtRxpcZJ1/bTePDgAcaOHYtnnnmmjiozfvq03bBhw5CUlITvvvsOFy9exLp169CuXbs6rNJ46dp+f/31F8aOHYvXXnsNZ8+exaZNm3DkyBFMnDixjis1Pvv27UNERAQOHz6MxMREqFQqhIaGaq0w/aiDBw9i5MiReO2113DixAkMHToUQ4cOxZkzZ+qxcunp03bJyckYOXIk9u7di0OHDsHHxwehoaG4detWPVZexwQyWgCELVu26Py+jh07CnPnzjV8QSZGl/YbPny4MHv2bCE6Olro2rVrndZlCmrSdn/88Yfg7Ows3L17t36KMiE1ab9FixYJLVu21Nq3dOlSwdvbuw4rMw2ZmZkCAGHfvn1VHjNs2DBh0KBBWvsCAgKESZMm1XV5Rq0mbfeo0tJSwdHRUVi7dm0dVla/2HNjZtRqNfLy8tCkSROpSzEZcXFxuHr1KqKjo6UuxaT89ttv6NmzJxYuXAhvb2+0bdsW7777LgoLC6UuzSQEBgbixo0b2LFjBwRBQEZGBjZv3oyBAwdKXZrkcnJyAKDa/44dOnQIwcHBWvvCwsJw6NChOq3N2NWk7R6lVCqhUqnM6veG5AtnkmF9/vnnyM/Px7Bhw6QuxSRcvnwZ7733Hvbv3w9LS/5z0MXVq1dx4MAB2NjYYMuWLcjOzsaUKVNw9+5dxMXFSV2e0QsKCsJPP/2E4cOHo6ioCKWlpRg8eLDOQ6rmRq1WY9q0aQgKCqp2QeT09HRxgWUNd3d3pKen13WJRqumbfeomTNnwsvLq0JYNGXsuTEj8fHxmDt3LjZu3Ag3NzepyzF6ZWVlGDVqFObOnYu2bdtKXY7JUavVkMlk+Omnn9C7d28MHDgQixcvxtq1a9l7UwPnzp3D1KlTMWfOHKSkpGDnzp1IS0vD5MmTpS5NUhEREThz5gzWr18vdSkmR5+2W7BgAdavX48tW7bAxsamDqurX/xfVTOxfv16vP7669i0aZNZpe+6lJeXh2PHjuHEiROIjIwE8PAXtiAIsLS0xK5du/Cf//xH4iqNl6enJ7y9veHs7Czu69ChAwRBwM2bN9GmTRsJqzN+8+fPR1BQEKZPnw4A6NKlC+zt7dG3b198/PHH8PT0lLjC+hcZGYlt27bhzz//RLNmzao91sPDAxkZGVr7MjIy4OHhUZclGi1d2k7j888/x4IFC7B792506dKljiusX+y5MQPr1q1DeHg41q1bh0GDBkldjslwcnLC6dOncfLkSXGbPHky2rVrh5MnTyIgIEDqEo1aUFAQbt++jfz8fHHfpUuXYGFhUeP/uDZkSqUSFhba/wmWy+UAAKGBLfknCAIiIyOxZcsW7NmzBy1atHjsewIDA5GUlKS1LzExEYGBgXVVplHSp+0AYOHChZg3bx527tyJnj171nGV9Y89N0YmPz8f//77r/g8NTUVJ0+eRJMmTdC8eXPMmjULt27dwvfffw/g4VDUuHHj8NVXXyEgIEAcb7a1tdX6P+qGQpf2s7CwqDAu7ebmBhsbG53Gq82Frn/3Ro0ahXnz5iE8PBxz585FdnY2pk+fjgkTJsDW1laqryEZXdtv8ODBmDhxIlasWIGwsDDcuXMH06ZNQ+/eveHl5SXV15BEREQE4uPj8euvv8LR0VH875izs7P4d2ns2LHw9vbG/PnzAQBTp05F//798cUXX2DQoEFYv349jh07hpUrV0r2PaSgT9t99tlnmDNnDuLj4+Hn5ye+x8HBAQ4ODtJ8EUOT8lItqmjv3r0CgArbuHHjBEEQhHHjxgn9+/cXj+/fv3+1xzc0urbfoxrypeD6tN358+eF4OBgwdbWVmjWrJkQFRUlKJXK+i/eCOjTfkuXLhU6duwo2NraCp6ensLo0aOFmzdv1n/xEqus3QAIcXFx4jH9+/ev8N+1jRs3Cm3bthWsra2FTp06Cdu3b6/fwo2APm3n6+tb6Xuio6Prvf66IhOEBtb/SURERGaNc26IiIjIrDDcEBERkVlhuCEiIiKzwnBDREREZoXhhoiIiMwKww0RERGZFYYbIiIiMisMN0RERGRWGG6IyKTJZLJqt5iYGKlLJKJ6xrWliMik3blzR3y8YcMGzJkzBxcvXhT3mc1aOURUYww3RGTSPDw8xMfOzs6QyWRa+4io4eGwFBEREZkVhhsiIiIyKww3REREZFYYboiIiMisMNwQERGRWWG4ISIiIrPCcENERERmRSYIgiB1EURERESGwp4bIiIiMisMN0RERGRWGG6IiIjIrDDcEBERkVlhuCEiIiKzwnBDREREZoXhhoiIiMwKww0RERGZFYYbIiIiMisMN0RERGRWGG6IiIjIrDDcEBERkVn5f1j2+68PuVlqAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "J=1\n", "T_crit=2.26918531421\n", "beta_min=1/(T_crit*J)\n", "N=100\n", "\n", "beta_list=np.linspace(beta_min,2*beta_min,N) \n", "y=[M_exact(x,J) for x in beta_list]\n", "plt.figure()\n", "plt.plot(beta_list, y,color='black' ,label='M(beta)')\n", "\n", "# Add labels and a legend\n", "plt.xlabel(r'$\\beta J$')\n", "plt.ylabel(r'$M(\\beta J)$')\n", "plt.title('Magentization')\n", "\n", "beta_c = 1/T_crit # critical beta\n", "plt.axvline(x=beta_c, color='black', linestyle='--', label=r'$\\beta_c \\,J\\approx$'+str(round(beta_c, 4) ))\n", "\n", "plt.legend()\n", "plt.grid(True) \n", "\n", "\n", "plt.figure()\n", "x=[1/T for T in beta_list]\n", "plt.plot(x, y,color='black' ,label='M(T)')\n", "\n", "# Add labels and a legend\n", "plt.xlabel('T')\n", "plt.ylabel('M(T)')\n", "plt.title('Magentization')\n", " \n", "plt.axvline(x=T_crit, color='black', linestyle='--', label=r'$T_c\\approx$'+str(round(T_crit,4)))\n", " \n", "plt.legend()\n", "plt.grid(True) " ] } ], "metadata": { "kernelspec": { "display_name": "base", "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": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 2 }