Ising model.ipynb

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   "source": [
    "<a href=\"https://colab.research.google.com/github/AliMdRamjan/Hello-world/blob/main/Ising_model.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Monte-Carlo simulation of 2D Ising model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " H= -J\\sum_{ij} {S_i}{S_j}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## The Ising Hamiltonian can be written as,\n",
    "                \n",
    "\n",
    "   H=−J∑⟨ij⟩SiSj\n",
    " \n",
    "- The spins  Si can take values  ±1,\n",
    "- ⟨ij⟩ implies nearest-neighbor interaction only,\n",
    "- J>0 is the strength of exchange interaction.\n",
    "The system undergoes a 2nd order phase transition at the critical temperature  Tc\n",
    " . For temperatures less than  Tc\n",
    " , the system magnetizes, and the state is called the ferromagnetic or the ordered state. This amounts to a globally ordered state due to the presence of local interactions between the spin. For temperatures greater than  Tc\n",
    " , the system is in the disordered or the paramagnetic state. In this case, there are no long-range correlations between the spins.\n",
    "\n",
    "The order parameter,\n",
    "                                           m=⟨S⟩/N,\n",
    "for this system is the average magnetization. The order parameter distinguishes the two phases realized by the systems.It is zero in the disordered state, while non-zero in the ordered, ferromagnetic, state.\n",
    "\n",
    "The one dimensional (1D) Ising model does not exhibit the phenomenon of phase transition while higher dimensions do. This can be argued based on arguments, due to Peierls, related to the net change in free energy, F=E−TS .Here  E and  S are, respectively, the energy and entropy of the system. We estimate the net change in free energy for introducing a disorder in an otherwise ordered system. The ordered state can only be stable if the net change in free energy is positive,  ΔF>0, for any non-zero temperature.\n",
    "\n",
    "- 1D Ising model:\n",
    "Introducing a domain wall (defect) in an ordered state increases the energy by  4J( where each site has two neighbors (left and right), the maximum difference in energy would be 4J)\n",
    " , while the entropy change is  kBlnN\n",
    " , due to  N\n",
    "  choices to introduce the domain. So net change in the free energy,  ΔF=4J−kBTlnN\n",
    " , is always negative for  N→∞\n",
    " . Thus, the system prefers a disordered state. So, there is no spontaneous symmetry breaking in 1D for an infinite Ising chain. This argument can be generalized for any domain of length  L\n",
    "  and higher dimensions.\n",
    "\n",
    "- 2D Ising model:\n",
    "For two and higher dimensions, we can introduce islands of defects, which cost only at the boundaries, and are thus, proportional to the perimeter  L=εN2\n",
    " , where  0<ε<1\n",
    " . In 2D, the number of islands scale as  3εN2\n",
    " , while  ΔE=ε4JN2\n",
    " .  ΔF\n",
    "  is then  ε4JN2−kBTln(N23εN2)\n",
    " . This gives a rough estimate of the critical temperature  Tc∼J/kB\n",
    " ."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code simulates the Ising model in 2D using the Metropolis algorithm with includes the following steps.\n",
    "\n",
    "- Prepare an initial configuration of N spins\n",
    "- Flip the spin of a randomly chosen lattice site.\n",
    "- Calculate the change in energy dE\n",
    "- If dE < 0, accept the move. Otherwise accept the move with probability exp^{-dE/T}. This satisfies the detailed balance condition, ensuring a final equilibrium state.\n",
    "- Repeat 2-4.\n",
    "\n",
    "In the code below, we have estimated and plotted energy, magnetization, specific heat and susceptibility of the system.\n",
    "Have a look here for better visualization, https://physics.weber.edu/schroeder/software/demos/IsingModel.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "0r6EyMsL85yz"
   },
   "outputs": [],
   "source": [
    "#importing necessary libraries for this simulation.\n",
    "import numpy as np\n",
    "from numpy.random import rand\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.sparse import spdiags,linalg,eye #computational efficiency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1, -1,  1, ..., -1,  1,  1],\n",
       "       [ 1, -1,  1, ..., -1,  1,  1],\n",
       "       [-1, -1,  1, ...,  1,  1, -1],\n",
       "       ...,\n",
       "       [-1,  1,  1, ..., -1, -1, -1],\n",
       "       [-1,  1, -1, ..., -1,  1,  1],\n",
       "       [-1,  1, -1, ..., -1,  1,  1]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state=2*np.random.randint(2, size=(N,N))-1  #The subtraction of 1 is performed to transform the array elements from {0, 2} to {-1, 1}\n",
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 1000)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 615
    },
    "id": "j9oTKGGQ9SN7",
    "outputId": "4ea05ced-0fc3-44f5-d893-e51f5ba0c973"
   },
   "outputs": [
    {
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JGjt2bJ17Ka5du1Z/+ctflJWVpQMHDmjx4sW67rrrqj3m448/1uTJk/Xll1+qXbt2evDBB3X33XfX6foAgNATnZio6MREOR0OlRYXK8pup2c6APiBt9Xmx48f19/+9jdJUpcuXfwZEgAAAFBnAU2oL126VOnp6Wrfvr3Gjh1b4/jmzZvr4Ycf1v79+9WiRQv9/Oc/r9N1jx8/rp49e+q2227TyJEjaxy/e/duXX311brjjjv0r3/9S+vXr9c999yj1q1be3U8ACB8WKxWEukA4AOdO3eudP/QoUPVuHHjao8tKSlRXl6enE6nDMPQ8OHD/REiAAAAUG8BTagvWrRIkjR69Givqs0bNWqkm266Sc8++6zefvvtOifU09LSlFaLxeVefvllnXfeeZoxY4Yk6aKLLlJmZqaeffZZEuoAAABAJb799tsK+0zT1L59+2p1nn79+unBBx/0UVQAAACAbwU0ob5161YZhqGBAwd6fczll1+uZ599Vps3b/ZjZOVt2LBBQ4cOLbfvZz/7mWbPnq1Tp07VWGEDAAAANDTjxo0rtz1v3jwZhqERI0aoWbNmVR5nGIaaNGmitm3bqn///hoyZEidFiWtqc1jenq65s2bV+6YSy+9VJ999lmtrwUAAICGK6AJ9e+//16SlJCQ4PUxHTp0kKRaV7bUR25urtq0aVNuX5s2bXT69GkdPnxYbdu2rXBMSUmJSkpKPNuFhYV+jxMAAAAIFXPmzCm37U5e//GPf1S3bt38fn1v2jwOGzasXJxWWn4BAACglgKaUD99+rQklUs818ThcEiSTpw44ZeYqnJ2VYxpmpXud5s+fboef/xxv8cFAAAAhIPHHntMkhQfHx+Q63nT5tFms+ncc88NSDwAAACITJZAXsxd9b1t2zavj9m6daskqXXr1n6JqTLnnnuucnNzy+3Ly8tTo0aN1LJly0qPmTJligoKCjyPvXv3BiJUAAAAICQ99thjeuyxx9SqVatgh+KxZs0axcfHKzExUXfccYfy8vKqHV9SUqLCwsJyDwAAADRsAU2o9+/fX6Zp6tVXX/X6mH/84x8yDEP9+vXzY2TlXXbZZVqxYkW5fcuXL1fv3r2r7J9us9kUGxtb7gEAAADgR6ZpaufOndq4caM2btyonTt3eu4E9be0tDS98cYbWr16tZ577jlt3LhRQ4YMqfbu2enTpysuLs7zqE3rSgAAAESmgCbUx44dK0nKzMzU/fffX+3k2TRN3X///crKyip3bF0cO3ZM2dnZys7OliTt3r1b2dnZ2rNnjyRXdfmtt97qGX/33Xfru+++0+TJk/X111/r9ddf1+zZs/Xb3/62zjEAAAAADdWyZcs0fPhwxcbGKjExUf369VO/fv2UmJio2NhYDR8+XMuWLfNrDKNHj9Y111yjpKQkz/W2b9+uDz74oMpjuAsVAAKnxOHUkcJSlTicwQ4FAKoV0B7qaWlpGjJkiFavXq0XX3xRn376qSZOnKiBAwd6Fvo8cOCA1q5dq7/97W/KysqSYRgaOHCgrr322jpfNzMzU1dccYVne/LkyZKkcePGae7cuTpw4IAnuS5JnTp10tKlS/Wb3/xGf//739WuXTu98MILVS5uBAAAAKCi48eP6+abb9b7778vSZUW1Bw/flxLly7V0qVLNWLECP3rX/9S06ZN/R5b27Zt1bFjR33zzTdVjrHZbLLZbH6PBQAasq07TmrR6iJ9urlYTlOyGFL/nnbdmBqrpC78DgYQegwzUPdYnnHkyBENHjxY27Ztq3KBTzfTNNW9e3d99NFHatGiRYAi9I3CwkLFxcWpoKCA9i8AAAARhHmed5xOpwYPHqz169fLNE01btxYQ4cOVd++fdWmTRuZpqm8vDxt3LhRy5cvl8PhkGEY+ulPf6o1a9bU+LdCdQzD0OLFi3XddddVOeaHH35Q+/bt9corr5S7W7U6fO8BwLeWrC3SzAVHFWWRSssUpru3J41prhEDY4IXIIAGozbzvIBWqEtSixYt9H//93966KGH9Oqrr+rEiROVjmvatKnuuusuPfnkk7Lb7QGOEgAAAEB9vPzyy1q3bp0Mw9DPfvYzvfbaa2rfvn2lY/ft26c77rhDGRkZWrdunV5++WX96le/qtX1jh07ph07dni23W0eW7RooRYtWmjatGkaOXKk2rZtq2+//VYPPfSQWrVqpeuvv75erxMAUDdbd5zUzAVHJZVPppfdnrHgqDq3t1KpDiCkBLxCvaz8/Hx99NFH+uKLL3T48GFJUqtWrZScnKwrrrhCcXFxwQqt3qheAQAAiEzM87zTr18/ff755+rbt68+/fRTWSzVL99UWlqqAQMGeI757LPPanW9NWvWlGvz6DZu3DjNmjVL1113nb744gvl5+erbdu2uuKKK/Tkk0/WaqFRvvcA4DuPvnJIG7YUV0imlxVlkfr3sOvxO1sHLjAADVJt5nlBTahHMibbAAAAkYl5nnfi4uJ07Ngxvfnmmxo9erRXx7z99tsaM2aMYmJiVFBQ4OcIa4/vPQD4RonDqWt+872cXmSkLIb0wV87yGat/oNZAKiP2szz+G0EAAAAwOfcPdATExO9PubCCy8sdywAIDIdP2l6lUyXJKfpGg8AoYKEOgAAAACf69KliyQpLy/P62PcY93HAgAiU9MmhixefnZqMVzjASBU+GVR0rVr13q+HjhwYKX766LsuQAAAACErptuuklffPGF5s+fr5/97GdeHTN//nwZhuF1ixgAQHiyWS3q39PudQ912r0ACCV+SagPHjxYhmHIMAydPn26wv66OPtcAAAAAELXxIkTtWDBAi1YsEA9e/bUgw8+WO34v/zlL3rrrbeUnJysSZMmBSZIAEDQjBoSo3XZxdWOKXVKo1JZswJAaPFLQl2SqlrrlDVQAQAAgMiXm5ur1157TXfddZemTJmit956S+PGjVOfPn0UHx8vwzB08OBBbdy4Uf/85z+VnZ2tPn366JVXXlFubm6V5z3vvPMC+CoAAP7S/YImmjSmuWYsOKooi8pVqru3J41prqQutuAFCQCV8EtC/aOPPqrVfgAAAACR5fzzzy93d+qWLVv0wAMPVHtMZmamkpOTq3yeu1YBILKMGBijzu2tWrSqUOs3F8tpunqm9+9h16jUWJLpAEKSXxLqgwYNqtV+AAAAAJGHu1MBADVJ6mJTUpfWKnE4dfykqaZNDHqmAwhpfkmo33DDDTIMQzNnzlSHDh38cQkAAAAAIWzOnDnBDgEAEEZsVots1mBHAQA180tC/d1335VhGHryySfL7bdYLLJYLNqyZYu6devmj0sDAAAACAHjxo0LdggAAACAz/n1HprKbvHktk8AAAAAAAAAQDjyS0I9JiZGknTw4EF/nB4AAAAAAAAAgIDzS8uXn/zkJ8rMzNTMmTPVt29fRUdHl3veMAx/XBYAAABACHI6nVqzZo02bNig3NxcnThxQk899ZTatm3rGeNwOHT69GlFRUXJZrMFMVoAAACgan5JqI8dO1YbN27Uf//7X7Vo0UJt2rRR48aNPc8PHTq03LY3DMPQzp07fR0qAAAAAD/64IMPNHHiRH377bfl9j/wwAPlEuqzZ8/Wfffdp+joaO3fv19NmzYNcKQAAABAzfySUP/1r3+t9evX65133tHp06e1b98+z3OmaZbb9hZV7QAAAEB4ee2113TXXXd51lFq1aqVDh8+XOnc/vbbb9cjjzyi/Px8LV68WL/85S8DHS4AAABQI78k1C0Wi95++21t2LBBK1eu1L59+1RSUqJ58+bJMAyNGDFCzZo188elAQAAAISAHTt26N5775UkDRkyRC+++KJ+8pOfyGKpfBknq9WqkSNH6rXXXtPy5ctJqAMAACAk+SWh7nbZZZfpsssu82zPmzdPkvTHP/5R3bp18+elAQAAAATRjBkzdOrUKSUlJWnp0qWyWq01HnP55ZfrtddeU3Z2tv8DBAAAAOqg8vIQAAAAAKiHVatWyTAMTZo0yatkuiR16dJFkrRnzx5/hgYAAADUmV8r1M/mdDoDeTkAAAAAQbJ3715J0iWXXOL1Me6FSE+cOOGPkAAAAIB6o0IdAAAAgM+5Fx51L0jqjUOHDkmSYmNj/RITAAAAUF8k1AEAAAD4XLt27SRJ27dv9/qYjz/+WJJ0/vnn+yMkAAAAoN780vJlyJAhklxVKatWraqwvy7OPhcAAACA0DVw4EB98803evPNN3XTTTfVOP7w4cP6xz/+IcMw6vV3AwAAAOBPfkmor1mzRtKPt3mW3W8YRq1u+3SPP/tcAAAAAELXnXfeqdmzZ2vp0qWaM2eObrvttirHfv/997rhhht0+PBhNWrUSHfeeWcAIwUAAAC855eE+sCBAytNgFe1HwAAAEBk6dOnj+6++269/PLLmjBhgpYuXapRo0Z5nt+yZYu2bt2q5cuXa8GCBTp58qQMw9ADDzygCy64IIiRAwAAAFUzzNqUi8NrhYWFiouLU0FBAYsqAQAARBDmed4rLS3V+PHj9c9//rPawhr3nyTp6emaPXt2yBbh8L0HAACITLWZ57EoKQAAAAC/iIqK0rx587Ro0SL16tVLpmlW+ujWrZvefPNNvf766yGbTAcAAAAkP7V8AQAAAAC3kSNHauTIkdq/f78yMzOVl5en0tJStWzZUr169VKXLl2CHSIAAADgFRLqAAAAAAKiXbt2GjFiRLDDAAAAAOosoC1ftm/frs6dOysxMVH79++vcfy+fft0wQUXqEuXLvruu+8CECEAAAAAAAAglTicOlJYqhKHM9ihAAghAa1QX7hwob799lsNGzZM7dq1q3F8+/btlZiYqA8//FALFizQ73//+wBECQAAAKC+SktLtX79eklSz549FRcXV+34/Px8bdmyRZI0cOBAv8cHAEBVtu44qUWri/Tp5mI5TcliSP172nVjaqySutiCHR6AIAtohfqHH34owzA0fPhwr4+59tprZZqmli5d6sfIAAAAAPjSypUrNXjwYI0cOVJWq7XG8VarVSNHjtQVV1yhjz76KAARAgBQ0ZK1Rbr/+Txt2OJKpkuS05Q2bCnWxOcO6r21RcENEEDQBTShvmfPHklSjx49vD4mKSmp3LEAACDwnA6HThUUyOlwBDsUAGHi7bffliSNGjVKdru9xvHnnHOORo8eLdM0tXDhQn+HBwBABVt3nNTMBUclSaVndXlxb89YcFTbdpYEODIAoSSgLV/y8vIkSdHR0V4f4x6bm5vrl5gAAEDVjuXkKC8jQ/lZWZJpSoahZikpik9LU3RiYrDDAxDCsrKyZBiGhgwZ4vUxV1xxhV566SV9/vnnfowMAIDKLVpdpChLxWR6WVEWadGqQiV1aR24wACElIBWqLv7JtYmOe4ee84559Tr2i+99JI6deqkJk2aKCUlRZ988km149944w317NlT55xzjtq2bavbbrtNP/zwQ71iAAAgnBxauVLbn3pK+Zs2uZLpkmSayt+0SduffFKHVq0KboAAQtr3338vSerUqZPXx5x//vmSpH379vkjJAAAqlTicOrTzcXVJtMlV7J9/eZiFioFGrCAJtQvvPBCSVJGRobXxyxbtkyS1KVLlzpfd+HChZo0aZIefvhhffHFF7r88suVlpZWZRuZdevW6dZbb9Xtt9+uL7/8UosWLdLGjRs1YcKEOscAAEA4OZaTo73z5rk2nGf9sXBme+/cuTq2fXuAIwMQLk6cOCFJMt0fyHnBPbawsNAvMQEAUJXjJ01Pz/SaOE3XeAANU0AT6j/72c9kmqZeeeUVff311zWO//LLL/Xqq6/KMAwNGzasztd9/vnndfvtt2vChAm66KKLNGPGDCUkJGjWrFmVjv/ss890/vnna+LEierUqZN++tOf6q677lJmZmadYwAAIJzkZWRIlhqmCRaL8s588A0AZ2vd2nUr/P/+9z+vj3GPbdmypV9iAgCgKk2bGLIY3o21GK7xABqmgCbUf/WrX6lp06Y6efKkhgwZovfff7/Kse+9956uvPJKFRcXy2636957763TNR0Oh7KysjR06NBy+4cOHapPP/200mP69++v77//XkuXLpVpmjp48KDeeecdXXPNNVVep6SkRIWFheUeAADURbAXAHU6HK6e6WdXplcY6FR+VhYLlQKoVJ8+fWSapubPn+/1MXPnzpVhGEpOTvZjZAAAVGSzWtS/p11RNWTKoizSgJ522awBTakBCCEBXZS0VatWevnll3XLLbcoLy9P1113nTp16qTLL79cbdu2lWEY2r9/vz755BPt3r1bpmnKMAzNmjVLbdq0qdM1Dx8+rNLS0grHt2nTpspe7v3799cbb7yh0aNH6+TJkzp9+rRGjBihv/3tb1VeZ/r06Xr88cfrFCMAAFLoLABaWlz8Y8/0mpimSouLZbFa/RsUgLDzi1/8Qv/5z3+0atUqPffcc3rggQeqHf/cc89p9erVMgxDo0aNClCUAAD8aNSQGK3LLq52TKlTGpUaG6CIAISigH+cdvPNN2vu3Lmy2+0yTVO7du3S/Pnz9cwzz+hPf/qT5s+fr127dsk0TTVt2lTz5s3TLbfcUu/rGkb5W3HcyfrKfPXVV5o4caIeffRRZWVlKSMjQ7t379bdd99d5fmnTJmigoICz2Pv3r31jhkA0HCE0gKgUXa7VMX/kRUYhms8AJxl9OjR6tmzp0zT1IMPPqiRI0fqk08+0alTpzxjTp8+rU8++UQ33HCDHnzwQRmGoaSkJP3yl78MYuQAgIaq+wVNNGlMc0mqUKnu3p40prmSutgCHBmAUBLQCnW3W2+9VVdddZVeeOEFLV26VNu2bfMsQGSxWNS9e3cNHz5c9913X50r091atWqlqKioCtXoeXl5VZ57+vTpGjBggH73u99Jknr06KGmTZvq8ssv11NPPaW2bdtWOMZms8lm4xcqAKD2vF0A1J6QEJBKdYvVqmYpKa7kfnVtXywWNUtOpjodQKUMw9DixYs1YMAAHThwQO+++67effddNW7cWC1atJBhGPrhhx88CXbTNNWuXTstWbKkysIXAAD8bcTAGHVub9WiVYVav7lYTtPVM71/D7tGpcaSTAcQnIS6JLVt21bTp0/X9OnTdfr0aR05ckSS1KJFCzVq5LuwrFarUlJStGLFCl1//fWe/StWrNC1115b6TEnTpyoEENUVJQkeRL/AAD4imcB0BqS13nLlgWs9Uv8sGHKr2kxbqdT8WlpAYkHQHg6//zz9cUXX+iuu+7Se++9J9M05XA4KhS7GIahG264QS+99JLi4+ODFC0AAC5JXWxK6tJaJQ6njp801bSJQc90AB5BS6iX1ahRI79OnCdPnqxbbrlFvXv31mWXXaZXXnlFe/bs8bRwmTJlivbt2+dZMGn48OG64447NGvWLP3sZz/TgQMHNGnSJPXt21ft2rXzW5wAgIbHswBoTR/YllkANBAV4dFduyohPV17586tmOw/s52Qnh7Q3u4AwlN8fLwWL16snJwcLV26VF988YUOHz4syXU3aXJysq655hpdeOGFQY4UAIDybFaLbNyMCeAsIZFQ97fRo0frhx9+0BNPPKEDBw4oKSlJS5cuVceOHSVJBw4c0J49ezzj09PTVVRUpBdffFEPPPCAmjVrpiFDhuiZZ54J1ksAAESoUF4AtHVqquwJCcpbtqz8QqnJyQFfKBVA+Ovatau6du0a7DAAAACAejHMIPUw2bFjh+bPn68NGzYoNzdXxcXFysjI0AUXXOAZs23bNu3Zs0dNmzbVoEGDghFmnRUWFiouLk4FBQWKjWX1ZwBA5ZwOh7InTPAuqW4YuuS114LSs9zpcKi0uFhRdjs909HgMc9ruPjeAwAARKbazPMC3gDK6XTqd7/7nS666CL98Y9/1KpVq/Tll19q9+7dcjgc5cbu3btXP//5z3XVVVdp3759gQ4VAAC/cy8AKksN/yVbLGqWklKrZLbT4dCpggI5z/r/tS4sVqsax8WRTAfgUyUlJVq1apUWLlyozz//vF7nWrt2rYYPH6527drJMAy9++675Z43TVPTpk1Tu3btZLfbNXjwYH355Zf1uiYAAAAanoAn1O+66y49//zzKi0tVbt27fSLX/yiyrFpaWnq3LmzSktL9c477wQwSgChypcJQiBUxA8bVv2CpFKtFgA9lpOjXTNnKnvCBG297z5lT5igXTNn6tj27T6IFgC889133+nBBx/Ugw8+qPz8/ArPf/bZZ+rSpYuGDh2qsWPH6rLLLlOfPn3KtWKsjePHj6tnz5568cUXK33+z3/+s55//nm9+OKL2rhxo84991xdddVVKioqqtP1AAAA0DAFNKG+Zs0azZ49W5L00EMP6dtvv9Xbb79d7TGjRo2SaZr66KOPAhEigBBFghCRzL0AqKSKlepntr1dAPTQypXa/tRTyt+06cc2Mqap/E2btP3JJ3Vo1SofRg4AVVu8eLGeffZZrV69Ws2aNSv3XFFRka677jodOHBApml6HllZWbrmmmt0+vTpWl8vLS1NTz31lG644YYKz5mmqRkzZujhhx/WDTfcoKSkJM2bN08nTpzQm2++WdeXCAAAgAYooAn1l19+WZJ09dVX66mnnlJUVFSNx/Tt21eSuB0TaMBIEKIhaJ2aqsSpU9UsOVkyDNfOMwuAJk6dqtapqTWe41hOjvbOm+faOLvi/cz23rlz+SAKQECsWLFChmHouuuuq/DcK6+8ory8PEnSxIkTtWTJEt1zzz2SpK+++krz3L/LfGT37t3Kzc3V0KFDPftsNpsGDRqkTz/9tMrjSkpKVFhYWO4BAACAhq1RIC+2YcMGGYah22+/3etjOnToIEnKzc31V1gAQpi3CUJ7QoJX1btAKItOTFR0YmKdFwDNy8hwVbRX1z7GYlHesmX8vADwu127dkmSUlJSKjz39ttvyzAMXX/99ZoxY4Ykafjw4Tp06JAWLVqkd955p1Z/M9TE/bdEmzZtyu1v06aNvvvuuyqPmz59uh5//HGfxQEAAIDwF9AKdXcVSqdOnbw+plEjV87/1KlTfokJQGjzJAircyZBCESKuiwA6nQ4lJ+V5VUv9vysLNYhAOB37rn/2UnswsJCbdq0SZJ02223lXtuzJgxkqTNmzf7JSbDfQfQGaZpVthX1pQpU1RQUOB57N271y9xAQAAIHwEtELdbrfL4XDoxIkTXh/jXpSoefPm/goLQIjyJAjdbV6qHPhjgrA2CUggkpQWF9f8s+JmmiotLubnBYBfuRf7LC0tLbd//fr1Ki0tVaNGjTR48OByzyUkJEiSjhw54tNYzj33XEmuSvW2bdt69ufl5VVI+Jdls9lks9l8GgsAAADCW0Ar1N2V6V988YXXx/z3v/+VJHXr1s0vMQEIXXVJEAINVZTd/mPv9ZoYhms8APhRXFycJGn//v3l9q9Zs0aS1LNnTzVt2rTSY5s0aeLTWDp16qRzzz1XK1as8OxzOBz6+OOP1b9/f59eCwAAAJEtoAn1oUOHyjRNvfLKK3LWdEu6pKysLP3zn/+UYRgaNmxYACIEEEpIEALes1itapaS4lWLpGYpKVSnA/C7pKQkSdLixYs9+0pLSz3906+44ooKx+zbt09SxTYx3jh27Jiys7OVnZ0tybUQaXZ2tvbs2SPDMDRp0iQ9/fTTWrx4sbZt26b09HSdc845Gjt2bB1eHQAAABqqgCbU77vvPtntdm3dulV33HFHtX3R//3vf2vYsGFyOByKjY3VnXfeGcBIAYQCEoRA7cQPG+ZVD/X4tLTABASgQbv++utlmqb++c9/6ve//73++9//auzYsZ5FQG+88cYKx2RmZkqSzjvvvFpfLzMzU7169VKvXr0kSZMnT1avXr306KOPSpIefPBBTZo0Sffcc4969+6tffv2afny5YqJianrSwSAsFXicOpIYalKHDUXOwIAyjNM09t+Cr4xe/Zs3XHHHTIMQ+3atdPw4cP18ssve6pGTpw4oZUrV2rXrl2eRYIWLFigUaNGBTLMeissLFRcXJwKCgoUGxsb7HCAsHUsJ0fbn3qqxnGJU6cqOjExABEBoe3QqlXaO3eu64Oossn1M9sJ6elqnZoatPiASMA8zzslJSVKTk7W119/XW7hT9M0NWLECL377rsVjklKStLXX3+tJ554Qg8//HAAo/UO33sA4W7rjpNatLpIn24ultOULIbUv6ddN6bGKqkLa0YAaLhqM88LeEJdkl5//XVNnDhRJ06cKDe5dnOHZLPZ9PLLL2vcuHGBDrHemGwDvkOCEKidY9u3K2/Zsh8X9TUMNUtJUXxaGh88AT7APM97ubm5uu+++/T+++/r1KlTslqtGj16tF588cUKleFr167V4MGDZRiGNmzYoL59+wYp6qrxvQcQzpasLdLMBUcVZZFKy/xZ5d6eNKa5Rgzkrh0ADVPIJ9Ql6fvvv9eMGTP03nvvaceOHeWea9++vUaMGKHf/e53Ov/884MRXr0x2QZ8iwQhQp3T4VBpcbGi7PaQaT8UijEBkYB5Xu2VlJToyJEjatmypaxV/D7avXu39uzZI0kaOHBgpYU3wcb3HkC42rrjpO5/Pq/GcS880IZKdQANUlgk1MsqLCxUXl6eSktL1bJlS7Vq1SrYIdUbk23AP0gQItQcy8lRXkYGH/YADQjzvIaL7z2AcPXoK4e0YUtxucr0s0VZpP497Hr8ztaBCwwAQkRt5nmNAhRTtWJjY5mQAvCKxWolkY6QcWjlSu2dN8/Vfsj9+bRpKn/TJuVnZtKOCAAAAEFX4nB6eqZXp9Qprd9crBKHUzarJTDBNSAlDqeOnzTVtInB+wuEuZBIqAPwHSq4gcA4lpPjSqZL5Xv7l9neO3eu7AkJVKoDAAAgaI6fNGtMprs5Tdd4G39K+gwLwQKRJ6gJ9aysLK1cuVLbtm3TkSNHJEktWrRQUlKSrrzySqWkpAQzPCCs0HYCCKy8jIyKC+WezWJR3rJl/AwCaJCGDBlS52MNw9CqVat8GA0ANFxNmxiyGPIqqW4xXOPhG2UXgnW//05T2rClWOuyi1kIFghTQUmoZ2Zm6t5771VmZmaVYx566CH17t1bf//739W7d+8ARgeEH9pOAIHldDh+/PCq2oFO5WdlyelwcMcIgAZnzZo1MgxD1S3ZdPbCo+6xobggKQCEK5vVov497V73UKcdiW9s3XFSMxcclaQK77t7e8aCo+rc3kqlOhBmAp5Qf/vtt3XLLbfo9OnTngmz1WpVixYtZJqmjh49KofDIUnauHGjBgwYoH/9618aNWpUoEMFwgJtJ4DAKy0urjmZ7maaKi0uJqEOoMEZOHBgjYnx48eP65tvvlFBQYEMw1BiYqLatm0boAgBoOEYNSRG67KLqx1T6pRGpbK+na8sWl2kKEvFZHpZURZp0apCJXVhIVggnAQ0of6///1P48aN06lTp9SoUSPdcccdGj9+vC655BJFRUVJkkpLS7V582bNnj1br776qk6dOqVbb71V3bt3109+8pNAhguEBdpOAIEXZbdLhuFdUt0wXOMBoIFZs2aNV+NM09QHH3yg+++/X0eOHNFrr72mn/70p/4NDgAamO4XNNGkMc0140z7kbJJXvf2pDHNqZT2ERaCBSJbQH9an3nmGZWUlKhJkyZavny5/v73vyslJcWTTJekqKgoJScn6+9//7tWrFihJk2ayOFw6M9//nMgQwXCgqftRHXJdKlc2wkA9WexWtUsJcX1YVa1Ay1qlpJCdToAVMMwDP385z/XunXrFBUVpeuvv1779u0LdlgAEHFGDIzRCw+0Uf8edlnO3EBkMVxtXl54oA29vH2oLgvBAggfAU2or1q1SoZhaNKkSRo8eHCN4wcNGqRJkybJNE2tXLnS/wECYaYubSdqw+lw6FRBAYl4oBLxw4Z59WFWfFpaYAICgDDXtm1bTZ48WT/88APFNADgJ0ldbHr8ztb64K8d9M6f2uuDv3bQ43e2pjLdx9wLwXqDhWCB8BPQhPqhQ4ckSVdffbXXx1xzzTXljgXwI0/bCW/Uou3EsZwc7Zo5U9kTJmjrffcpe8IE7Zo5U8e2b69HtEBkie7aVQnp6a6NsyvVz2wnpKfTagkAasHd6uWDDz4IciQAENlsVotaxEbRZsRP3AvBRtXw9kZZpAE9WQgWCDcB7aHeunVr7du3T02aNPH6GJvN9Slpq1at/BUWELbcbSfyN22qsYd6s+Rkr9pOHFq50rXIqcXyY/W7aSp/0yblZ2YqIT1drVNTffQKgPDWOjVV9oQE5S1b5mq/ZJqSYahZcrLi09JIpgNALVnPzFX2798f5EgAAKgfFoIFIldAE+oDBgzQ22+/rY0bN6p3795eHfP5559LEgsTAVWIHzZM+ZmZ1Q/ysu3EsZwcVzL9zDFnn0OS9s6dK3tCAolC4IzoxERFJybK6XCotLhYUXY7PdMBoI7WrVsnSTrnnHOCHAkAAPXDQrBA5AroPSWTJ09WVFSUnn76aa9auOTl5Wn69Olq3LixfvOb3wQgQiD8+LLtRF5GhleLLOYtW1aHSIHIZrFa1TgujmQ6ANTRhg0b9MQTT8gwDPXt2zfY4QAAUG8sBAtEpoBWqPfp00f/+Mc/dPfdd+vSSy/V888/rxEjRshyVgLP6XTq/fff1+TJk3Xo0CHNmjWLSTVQDV+0nXA6HD8eW+1Ap/KzsuR0OEgcAgCAKj3xxBM1jnE6nTp69KgyMzP1f//3f3I6nTIMg2IaAEDESOpiU1KX1ipxOHX8pKmmTQx6pgNhLqAJ9fHjx0uSunXrps2bN2vkyJFq3ry5evXqpfj4eBmGoYMHDyo7O1tHjhyRJPXs2VPr1q3z3P55NsMwNHv27IC9BiBU1bftRGlxcc3JdDfTVGlxMQl1AABQpWnTpsnwdvF0SaZpqlGjRvrzn/+sq666yo+RAQAQeDarRTb+hAYiQkAT6nPnzvVMqg3DkGmaOnLkiFavXl1unHkmqWcYhjZv3qzNmzdXej7TNEmoA2exWK11SnRH2e2SYXiXVDcM13gAAIBqmDXMKwzDUExMjDp16qRBgwbpzjvvVLdu3QIUHQAAAFB7AU2on3feebWqUgEQOBarVc1SUpS/aVPFBUnLDbSoWXIy1ekAAKBazurmEwAAAECYCmhC/dtvvw3k5QDUUvywYcrPzKx+kNOp+LS0wAQEAAAAAAAAhBBWQQDgEd21qxLS010bZy0W7N5OSE/3apFTAACAmvzwww86evRosMMAAAAAvEZCHUA5rVNTlTh1qpolJ7t6qkuSYahZcrISp05V69TU4AYIAADC2sGDB3XnnXeqVatWio+PV6tWrdS8eXOlp6drz549wQ4PAAAAqFZAW75444cffpDFYlHz5s2DHQrQYEUnJio6MVFOh0OlxcWKstvpmQ4AAKqUm5ur5ORkSdLUqVP1q1/9qtJxu3bt0sCBA3XgwIFyC5YWFBTon//8p95//32tWrVKl1xySSDCBgAAAGotJCrUA1Gl8tJLL6lTp05q0qSJUlJS9Mknn1Q7vqSkRA8//LA6duwom82mLl266PXXX/dJLEC4sFitahwXRzIdAABU6+OPP1Zubq6OHDmiG2+8scpxY8aM0f79+z3J9ISEBF166aWKiYmRaZo6evSobrrpJp0+fTpQoQMAAAC14reEem5urtq1a6d27dpp1qxZVY7btWuXUlJSNHv2bB05ckSmaco0TU+VSq9evZSdnV2vWBYuXKhJkybp4Ycf1hdffKHLL79caWlp1Sbrb7zxRq1atUqzZ89WTk6O3nrrLf3kJz+pVxwAAABAJFqzZo0k6YorrlDLli0rHfPf//5XmZmZMgxDLVq0UEZGhr777jtt2LBBubm5uu222yRJ27dv17///e9AhQ4AQINV4nDqSGGpShzOYIcChBW/tXxxV6lYrVavqlTcEhIS1K5dO3311VcqKiryVKls3bpVjRrVLdznn39et99+uyZMmCBJmjFjhj788EPNmjVL06dPrzA+IyNDH3/8sXbt2qUWLVpIks4///w6XRsAAACIdJs3b5ZhGLrqqquqHPPGG294vn7uuec0dOhQz7bdbtdrr72mzMxMbdu2TUuWLNHo0aP9GjMAAA3V1h0ntWh1kT7dXCynKVkMqX9Pu25MjVVSF1uwwwNCnt8q1EOlSsXhcCgrK6vchF2Shg4dqk8//bTSY9577z317t1bf/7zn9W+fXslJibqt7/9rYqLi+sUAwAAABDJDh48KEnq2bNnlWPcfx/ExcVp7NixFZ43DEPjx4+XaZravHmzX+IEAKChW7K2SPc/n6cNW1zJdElymtKGLcWa+NxBvbe2KLgBAmHAbwl1X1WpdO/eXZK0ZMmSOsVx+PBhlZaWqk2bNuX2t2nTRrm5uZUes2vXLq1bt07btm3T4sWLNWPGDL3zzju69957q7xOSUmJCgsLyz0AAACAhiAvL0+S1KpVq0qf37Vrlw4ePCjDMHT55ZercePGlY7r1auXJJW7gxUAgNqgjUnVtu44qZkLjkqSSs96e9zbMxYc1badJQGODAgvfmv54ssqld/85jf1rlIxDKPctmmaFfa5OZ1OGYahN954Q3FxcZJcbWN+8Ytf6O9//7vsdnuFY6ZPn67HH3+8XjEi/DgdDpUWFyvKbmfhTgAA0GC5FxF1OByVPv9///d/nq9TUlKqPE+zZs0kScePH/ddcACABoE2JjVbtLpIUZaKyfSyoizSolWFSurSOnCBAWHGbwn1UKlSadWqlaKioipUo+fl5VWoWndr27at2rdv70mmS9JFF10k0zT1/fff68ILL6xwzJQpUzR58mTPdmFhoRISEuoUM0LfsZwc5WVkKD8rSzJNyTDULCVF8Wlpik5MDHZ4ANAg8KEmEDpatWql/fv3a/v27erTp0+F5zds2OD5unfv3lWep6jIdZt5kyZNfB8kACBiLVlbpJkLjirKogptTNZlF2vSmOYaMTAmuEEGWYnD6fmwoTqlTmn95mKVOJyyWf3W2AIIa35LqIdKlYrValVKSopWrFih66+/3rN/xYoVuvbaays9ZsCAAVq0aJGOHTum6OhoSa4+7haLRR06dKj0GJvNJpuNTzwbgkMrV2rvvHmSxeJKpkuSaSp/0yblZ2YqIT1drVNTgxskAEQwPtQEQk/Pnj21f/9+/fvf/9bNN99c7jnTNPX+++9LkiwWiwYMGFDleb777jtJqrLwBQCAs3nbxqRze2uDrlQ/ftKsMZnu5jRd423UrACV8ttHTe7K9O3bt1f6fCCrVCZPnqzXXntNr7/+ur7++mv95je/0Z49e3T33XdLclWX33rrrZ7xY8eOVcuWLXXbbbfpq6++0tq1a/W73/1O48ePr7TdCxqOYzk5rmS6JDnP+p/6zPbeuXN1rIp/9wCA+jm0cqW2P/WU8jdtqvCh5vYnn9ShVauCGyDQQF177bUyTVNLlizR/Pnzyz33l7/8Rd99950Mw1Bqamq5u0DP5v4boWvXrn6NFwAQOdxtTKrjbmPSkDVtYshSeefjCiyGazyAyvktoe7unf7vf/+7wnOBrlIZPXq0ZsyYoSeeeEKXXHKJ1q5dq6VLl6pjx46SpAMHDmjPnj2e8dHR0VqxYoXy8/PVu3dv3XzzzRo+fLheeOGFOseAyJCXkeGqTK+OxaK8ZcsCExAANCB8qAmErptvvtkzt77tttt06aWX6uabb1ZycrKmTJniGVe2ReLZTNPUu+++K8Mw1K9fP7/HDAAIf+42JtX1BJfKtzFpqGxWi/r3tHv14cOAnnbavQDV8FvLl2uvvVZLly71VKmUrQAPRpXKPffco3vuuafS5+bOnVth309+8hOtWLGiXtdEZHE6HD+2F6h2oFP5WVlyOhz09AUAH/J8qHl2Mr2sMx9q0voFCKxzzjlHCxcu1NChQ1VYWKjMzExlZmZKciXKJWn8+PEaOnRoledYunSp9u3bJ8MwdOWVVwYkbgBAeKONSe2MGhKjddnF1Y4pdUqjUmMDFBEQnvz2cRNVKog0pcXFNSfT3UzTNR4A4BOeDzWrS6ZL5T7UBBBYffv2VVZWlkaNGiW73S7TNGWapjp27Khnn31Wr7zySrXHP/nkk5Kkc889l7k/AMArtDGpne4XNNGkMc0lqUKlunt70pjmDbrXPOANv1WoU6WCSBNlt0uG4V1S3TBc4wEAPlGXDzW5SwgIvC5dumjhwoVyOp06dOiQrFarmjdv7tWxq86sgdCokd/+RAEARBh3G5MNW6pv+xJlkfr3oI2JJI0YGKPO7a1atKpQ6zcXy2m6Pmzo38OuUamxJNMBL/h1tuquUnnooYf0wQcf6MSJE5Kkjh076te//rV+85vfVHs8VSoIJRarVc1SUlwL4dXQbqBZcjKJHADwIT7UBMKLxWKp9RpITZs29VM0AIBIRhuT2kvqYlNSl9YqcTh1/KSppk0MPmwAasHv5R9UqSCSxA8bpvwzd1pUyelUfFpaYAICgAaCDzUBAABQGXcbkxkLjirKonKV6u5t2phUzma1NOie8kBdBezjJ3eVirfJdMlVpdK0aVPZbPzSQ2iI7tpVCenprg3LWT8+Z7YT0tNZDA8A/CB+2DCveqjzoSYAAAgVJQ6njhSWqsRRwxwG9TJiYIxeeKCN+vewe3qqu9uYvPBAG40YGBPcAOE1fmYQDij9BmqpdWqq7AkJylu2zLVAnmlKhqFmycmKT0sjmQ4AfuL+UHPv3LmuDzHLJtfPbPOhJgAACAVbd5zUotVF+rRsj+qedt1Ij2q/oY1JeONnBuHEME1vV/hCbRQWFiouLk4FBQWKjaVPV6RyOhwqLS5WlN1OewEA8FJ9f3ce27694oeaKSl8qImAYZ7XcPG9B+CNJWuLNLOG9iNUTAM/4mcGoaA28zwq1IF6sFitJNIBwEvHcnKUl5FR70R4dGKiohMT+VATAACEnK07TmrmgqOSyicGy27PWHBUndtbqboFFB4/M9z1gLORUAcAAH53aOVK7Z03z9WaxX1znGkqf9Mm5WdmKiE9Xa1TU2t1Tj7UBAAAoWbR6qIKVbZni7JIi1YVKqlL68AFBoSoUP6ZoQ0NqsLHKgAAwK+O5eS4kulSxUVFz2zvnTtXx7ZvD3BkABqSadOmyTCMco9zzz032GEBiCAlDqc+3VxcbWJQciUO128uZtFFNHih/DOzZG2R7n8+Txu2uJLpkuQ0pQ1bijXxuYN6b21RwGJB6CGhDgAA/CovI8NVmV4di0V5y5YFJiA/cjocOlVQIKfDEexQAFTi4osv1oEDBzyPrVu3BjskABHk+EnTk3iridN0jQcaslD9mfG2Dc22nSUBiQehh5YvAADAb5wOx48906sd6FR+VpacDkdYtnHxVX94AP7VqFEjqtIB+E3TJoYshrxKEFoM13igtiKpn3eo/syEchsahAYS6gAAwG9Ki4trTqa7maZKi4vDLqHuj/7wAPzjm2++Ubt27WSz2XTppZfq6aefVufOnascX1JSopKSH6vPCgsLAxEmgDBls1rUv6ddG7ZU38IiyiL172EP+2QoAisS+3mH4s+Muw1NTUn+sm1o+FluePiOAwAAv4my2yXDy0oSw3CNDyP0hwfCx6WXXqr58+frww8/1Kuvvqrc3Fz1799fP/zwQ5XHTJ8+XXFxcZ5HQkJCACMGEI5GDYnxqh/0qNTYwASEiBDJ/bxD7WcmVNvQILSQUAcAAH5jsVrVLCXFqx7qzVJSwq46vSH1hwfCXVpamkaOHKnu3bvryiuv1AcffCBJmuf+UKwSU6ZMUUFBgeexd+/eQIULIEx1v6CJJo1pLslVVVuWe3vSmOZhW1GMwIv0ft6h9jPjbkPjDVo3NVy0fAEAAH4VP2yY8jMzqx/kdCo+LS0wAflIQ+kPD0Sqpk2bqnv37vrmm2+qHGOz2WSzkfQCUDsjBsaoc3urFq0q1Pqy7Tl62DUqjNtzIDgaQj/vUPqZCcU2NAg9JNQBAIBfRXftqoT0dO2dO9dVzV22NcqZ7YT09LBbvLMh9IcHIllJSYm+/vprXX755cEOBUAESupiU1KX1hG1gCQCryH18w6ln5lRQ2K0Lru42jG0bmrYSKgDAAC/a52aKntCgvKWLfuxqtsw1Cw5WfFpaUFPpjsdDpUWFyvKbvc66e3pD+9NUj0M+8MDkea3v/2thg8frvPOO095eXl66qmnVFhYqHHjxgU7NAARzGa1yMbn6aijuvTzDvd/b6HwM+NuQzNjwdEKdwe4t2nd1LCRUAcAAAERnZio6MTEOiWv/eVYTo7yMjLKJ/lTUrxK8rv7w+dv2lRxQdJyAy1qlpwc9NcKNHTff/+9brrpJh0+fFitW7dWv3799Nlnn6ljx47BDg0AgEq5+3l7k1Snn3dF9al2D6U2NAg9JNQBAEBAWazWkEguH1q5UnvnzXO1nXFXmZum8jdtUn5mphLS09U6NbXac0Rqf3ggEi1YsCDYIQAAUCv0866brTtOatHqIk+7HIsh9e9p1421TISHUhsahBb+FQAAgAbnWE6OK5kuVawuP7O9d+5cHdu+vdrzuPvDS3Il5ss6sx2O/eEBAAAQGkYNiak2mS7Rz7usJWuLdP/zedqw5cfe805T2rClWBOfO6j31hbV+pw2q0UtYqNIpsODfwkAAKDBycvIqJgAP5vForxly2o8V+vUVCVOnapmycmunuqSpz984tSpNVa5AwAAAFVx9/OWXJXoZbm3g93Pu8Th1JHCUpU4asj8+9nWHSc1c8FRSarwIYR7e8aCo9q2syTAkSHS0PIFAAA0KE6H48ee6dUOdCo/K0tOh6PGFjWh2B8eAAAAkSFU+3n7qrWKryxaXVRhEdGzRVmkRasKldSldeACQ8QhoQ4AABqU0uLimpPpbqap0uJir5PjodIfHgAAAJEl1Pp5L1lbpJkLjirKogqtVdZlF2vSmOYaMTAmYPGUOJyexH51Sp3S+s3FKnE4aeGCOuNfDgAAaFCi7PYfW7PUxDBc4wEAAIAQEAr9vEOxtcrxk2aNyXQ3p+kaH85Cpc1OQ0WFOgAAaFAsVquapaQof9OmiguSlhtoUbPkZCrOAQAAgDJCsbVK0yaGLIa8SqpbDNf4cBRqbXYaKirUAQBAgxM/bFj1yXRJcjoVn5YWmIAAAACAMOBurVJdMl0q31olEGxWi/r3tFdYuPVsURZpQE97WLZ7WbK2SPc/n6cNW4ortNmZ+NxBvbe2KLgBNiDh968HAACgnqK7dlVCerprw3LWdOjMdkJ6uqITEwMbGAAAABDCQrm1yqghMV4l+kelxgYmoErUtVVLKLbZacho+QIAABqk1qmpsickKG/ZMuVnZbkWKjUMNUtOVnxaGsl0AAAA4Cyh3Fql+wVNNGlMc804s1hq2cSze3vSmOZBaY1S31YtodhmpyEjoQ4AABqs6MRERScmyulwqLS4WFF2Oz3TAQAAgCq4W6ts2FJ925coi9S/R+Bbq4wYGKPO7a1atKpQ68smr3vYNSpIfcaXrC3SzDNJ/rNbtazLLtakMc01YmBMlce72+zU9CFG2TY74djSJpyQUAcAAA2exWolkQ4AAAB4YdSQGK3LLq52TDBbqyR1sSmpS2uVOJw6ftJU0yZG0BLM3rZq6dzeWmWyvy5tdmz8aeNXfFwBAAAAAAAAwCvu1iqSKiwC6t4OVmuVsmxWi1rERgW1WtvdqqU67lYtVXG32fFGoNvsNFRUqAMAAAAAAADwWii2Vgk1vmrVEuptdhoiEupACKB3LwAAAAAACCeh1FolFPmyVYs/2+zw/as9EupAEB3LyVFeRobys7Ik05QMQ81SUhSflqboxMRghwcAAAAAAFAtm9VCz+5KuFu1eJNUr6lVi7vNzowzi5uWrVR3b9e2zc7WHSe1aHWRp4reYkj9e9p1I3cY1KjBfOzw0ksvqVOnTmrSpIlSUlL0ySefeHXc+vXr1ahRI11yySX+DRANzqGVK7X9qaeUv2mTK5kuSaap/E2btP3JJ3Vo1argBggAAAA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      "text/plain": [
       "<Figure size 1800x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##  BLOCK OF FUNCTIONS USED IN THE MAIN CODE\n",
    "def initialstate(N):   \n",
    "    state = 2*np.random.randint(2, size=(N,N))-1  #random spin configur....\n",
    "    return state\n",
    "\n",
    "def mcmove(config, beta):\n",
    "    '''\n",
    "    Monte Carlo move using Metropolis algorithm \n",
    "    '''\n",
    "    \n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "                a = np.random.randint(0, N)\n",
    "                b = np.random.randint(0, N)\n",
    "                s =  config[a, b]\n",
    "                nb = config[(a+1)%N,b] + config[a,(b+1)%N] + config[(a-1)%N,b] + config[a,(b-1)%N]\n",
    "                cost = 2*s*nb\n",
    "                \n",
    "                if cost < 0:\n",
    "                    s *= -1\n",
    "                elif rand() < np.exp(-cost*beta):\n",
    "                    s *= -1\n",
    "                config[a, b] = s\n",
    "    return config\n",
    "\n",
    "\n",
    "\n",
    "def calcEnergy(config):\n",
    "    '''\n",
    "    Energy of a given configuration\n",
    "    '''\n",
    "    energy = 0 \n",
    "    \n",
    "    for i in range(len(config)):\n",
    "        for j in range(len(config)):\n",
    "            S = config[i,j]\n",
    "            nb = config[(i+1)%N, j] + config[i,(j+1)%N] + config[(i-1)%N, j] + config[i,(j-1)%N]\n",
    "            energy += -nb*S\n",
    "    return energy/2.  # to compensate for over-counting\n",
    "\n",
    "\n",
    "\n",
    "def calcMag(config):\n",
    "    '''\n",
    "    Magnetization of a given configuration\n",
    "    '''\n",
    "    mag = np.sum(config)\n",
    "    return mag\n",
    "## NOTE: change these parameters for a smaller and faster simulation \n",
    "#----------------------------------------------------------------------\n",
    "\n",
    "\n",
    "nt      = 32         #  number of temperature points\n",
    "N       = 10         #  size of the lattice, N x N\n",
    "eqSteps = 2**8       #  number of MC sweeps for equilibration\n",
    "mcSteps = 2**9       #  number of MC sweeps for calculation\n",
    "\n",
    "\n",
    "T       = np.linspace(1.53, 3.28, nt); \n",
    "E,M,C,X = np.zeros(nt), np.zeros(nt), np.zeros(nt), np.zeros(nt)\n",
    "n1, n2  = 1.0/(mcSteps*N*N), 1.0/(mcSteps*mcSteps*N*N) \n",
    "# divide by number of samples, and by system size to get intensive values\n",
    "#  MAIN PART OF THE CODE\n",
    "#----------------------------------------------------------------------\n",
    "\n",
    "\n",
    "for tt in range(nt):\n",
    "    config = initialstate(N)         # initialise\n",
    "\n",
    "    E1 = M1 = E2 = M2 = 0\n",
    "    iT=1.0/T[tt]; iT2=iT*iT;\n",
    "    \n",
    "    for i in range(eqSteps):         # equilibrate\n",
    "        mcmove(config, iT)           # Monte Carlo moves\n",
    "\n",
    "    for i in range(mcSteps):\n",
    "        mcmove(config, iT)           \n",
    "        Ene = calcEnergy(config)     # calculate the energy\n",
    "        Mag = calcMag(config)        # calculate the magnetisation\n",
    "\n",
    "        E1 = E1 + Ene\n",
    "        M1 = M1 + Mag\n",
    "        M2 = M2 + Mag*Mag \n",
    "        E2 = E2 + Ene*Ene\n",
    "\n",
    "\n",
    "    # divide by number of sites and iteractions to obtain intensive values    \n",
    "    E[tt] = n1*E1\n",
    "    M[tt] = n1*M1\n",
    "    C[tt] = (n1*E2 - n2*E1*E1)*iT2\n",
    "    X[tt] = (n1*M2 - n2*M1*M1)*iT\n",
    "#  plot the calculated values   \n",
    "#----------------------------------------------------------------------\n",
    "\n",
    "f = plt.figure(figsize=(18, 10)); #  \n",
    "\n",
    "\n",
    "sp =  f.add_subplot(2, 2, 1 );\n",
    "plt.scatter(T, E, s=50, marker='o', color='IndianRed')\n",
    "plt.xlabel(\"Temperature (T)\", fontsize=20);\n",
    "plt.ylabel(\"Energy \", fontsize=20);         plt.axis('tight');\n",
    "\n",
    "\n",
    "sp =  f.add_subplot(2, 2, 2 );\n",
    "plt.scatter(T, abs(M), s=50, marker='o', color='RoyalBlue')\n",
    "plt.xlabel(\"Temperature (T)\", fontsize=20); \n",
    "plt.ylabel(\"Magnetization \", fontsize=20);   plt.axis('tight');\n",
    "\n",
    "\n",
    "sp =  f.add_subplot(2, 2, 3 );\n",
    "plt.scatter(T, C, s=50, marker='o', color='IndianRed')\n",
    "plt.xlabel(\"Temperature (T)\", fontsize=20);  \n",
    "plt.ylabel(\"Specific Heat \", fontsize=20);   plt.axis('tight');   \n",
    "\n",
    "\n",
    "sp =  f.add_subplot(2, 2, 4 );\n",
    "plt.scatter(T, X, s=50, marker='o', color='RoyalBlue')\n",
    "plt.xlabel(\"Temperature (T)\", fontsize=20); \n",
    "plt.ylabel(\"Susceptibility\", fontsize=20);   plt.axis('tight');\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 639
    },
    "id": "3dmSNviw-iCP",
    "outputId": "0db2b82f-6e19-4328-f977-d98d8f1fb0c0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x1200 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# Simulating the Ising model\n",
    "\n",
    "\n",
    "class Ising():\n",
    "    ''' Simulating the Ising model '''    \n",
    "    \n",
    "    \n",
    "    ## monte carlo moves\n",
    "    def mcmove(self, config, N, beta):\n",
    "        ''' This is to execute the monte carlo moves using \n",
    "        Metropolis algorithm such that detailed\n",
    "        balance condition is satisified'''\n",
    "        for i in range(N):\n",
    "            for j in range(N):            \n",
    "                    a = np.random.randint(0, N)\n",
    "                    b = np.random.randint(0, N)\n",
    "                    s =  config[a, b]\n",
    "                    nb = config[(a+1)%N,b] + config[a,(b+1)%N] + config[(a-1)%N,b] + config[a,(b-1)%N]\n",
    "                    cost = 2*s*nb\n",
    "                    if cost < 0:\t\n",
    "                        s *= -1\n",
    "                    elif rand() < np.exp(-cost*beta):\n",
    "                        s *= -1\n",
    "                    config[a, b] = s\n",
    "        return config\n",
    "    \n",
    "\n",
    "    \n",
    "    def simulate(self):   \n",
    "        ''' This module simulates the Ising model'''\n",
    "        N, temp     = 64, .4        # Initialse the lattice\n",
    "        config = 2*np.random.randint(2, size=(N,N))-1\n",
    "        f = plt.figure(figsize=(15, 15), dpi=80);    \n",
    "        self.configPlot(f, config, 0, N, 1);\n",
    "        \n",
    "        msrmnt = 1001\n",
    "        for i in range(msrmnt):\n",
    "            self.mcmove(config, N, 1.0/temp)\n",
    "            if i == 1:       self.configPlot(f, config, i, N, 2);\n",
    "            if i == 4:       self.configPlot(f, config, i, N, 3);\n",
    "            if i == 32:      self.configPlot(f, config, i, N, 4);\n",
    "            if i == 100:     self.configPlot(f, config, i, N, 5);\n",
    "            if i == 1000:    self.configPlot(f, config, i, N, 6);\n",
    "                 \n",
    "                    \n",
    "    def configPlot(self, f, config, i, N, n_):\n",
    "        ''' This modules plts the configuration once passed to it along with time etc '''\n",
    "        X, Y = np.meshgrid(range(N), range(N))\n",
    "        sp =  f.add_subplot(3, 3, n_ )  \n",
    "        plt.setp(sp.get_yticklabels(), visible=False)\n",
    "        plt.setp(sp.get_xticklabels(), visible=False)      \n",
    "        plt.pcolormesh(X, Y, config, cmap=plt.cm.RdBu);\n",
    "        plt.title('Time=%d'%i); plt.axis('tight')    \n",
    "    plt.show()\n",
    "rm = Ising()\n",
    "rm.simulate()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 639
    },
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   "source": [
    "# This example uses the 5-point Laplacian discretization from \n",
    "# [here](https://github.com/ketch/finite-difference-course)\n",
    "#\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "a,b, k = 0, 1.0, 100.0\n",
    "dh, dt = 1.0, 1e-3\n",
    "Ng, Tf = 256, 10001\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "class TDGL():\n",
    "    '''\n",
    "    Class to solve a PDE \n",
    "    '''\n",
    "    \n",
    "    def mu(self, u):\n",
    "        return a*u + b*u*u*u \n",
    "\n",
    "    \n",
    "    \n",
    "    def laplacian(self, Ng):\n",
    "        '''Construct a sparse matrix that applies the 5-point Laplacian discretization'''\n",
    "        e=np.ones(Ng**2)\n",
    "        e2=([1]*(Ng-1)+[0])*Ng\n",
    "        e3=([0]+[1]*(Ng-1))*Ng\n",
    "        h=dh\n",
    "        A=spdiags([-4*e,e2,e3,e,e],[0,-1,1,-Ng,Ng],Ng**2,Ng**2)\n",
    "        A/=h**2\n",
    "        return A\n",
    "\n",
    "    \n",
    "    \n",
    "    def integrate(self, L, x, y, u):\n",
    "        '''  simulates the equation and plots it at different instants '''\n",
    "        \n",
    "        f = plt.figure(figsize=(15, 15), dpi=80);    \n",
    "\n",
    "        for i in range(Tf):          \n",
    "            u = u - dt*(self.mu(u) - k*L.dot(u))\n",
    "            \n",
    "            if (i==0):      self.configPlot(x, y, u, f, 1, i);\n",
    "            if (i==1):      self.configPlot(x, y, u, f, 2, i);\n",
    "            if (i==10):     self.configPlot(x, y, u, f, 3, i);\n",
    "            if (i==100):    self.configPlot(x, y, u, f, 4, i);\n",
    "            if (i==1000):   self.configPlot(x, y, u, f, 5, i);\n",
    "            if (i==10000):  self.configPlot(x, y, u, f, 6, i);\n",
    "   \n",
    "\n",
    "\n",
    "    def configPlot(self, x, y, u,f, n_, i):\n",
    "        U= u.reshape((Ng, Ng))\n",
    "        sp =  f.add_subplot(3, 3, n_ )  \n",
    "        plt.setp(sp.get_yticklabels(), visible=False)\n",
    "        plt.setp(sp.get_xticklabels(), visible=False)\n",
    "        plt.pcolormesh(x,y,U, cmap=plt.cm.RdBu);\n",
    "        plt.title('Time=%d'%i)\n",
    "    plt.show()\n",
    "rm = TDGL()   # instantiate the class\n",
    "\n",
    "# generate the grid and initialise the field\n",
    "x = np.linspace(-1,1,Ng)\n",
    "y = np.linspace(-1,1,Ng)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "u=np.random.randn(Ng*Ng, 1);  # Initial data\n",
    "L = rm.laplacian(Ng)         # construct the laplacian\n",
    "rm.integrate(L, x, y, u)    # simulate\n",
    "\n",
    "#simulation completed!!"
   ]
  }
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