11_02_Ising2D.ipynb

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    "Simulation of the 2D Ising model\n",
    "--------------------------------\n",
    "\n",
    "One of the most interesting phenomena in nature is ferromagnetism. A FM\n",
    "material exhibits a non-zero spontaneous magnetization in the absence of\n",
    "an applied magnetic field. This occurs below a well-defined critical\n",
    "temperature $T_c$ known as the Curie temperature. For $T > T_c$ the\n",
    "magnetization vanishes. Hence $T_c$ separates two phases, a disordered\n",
    "one for $T>T_c$, and a ferromagnetic one for $T<T_c$.\n",
    "\n",
    "Although the Ising model is too simple, it already contains much of the\n",
    "physics of the FM phase transition. In order to explore the properties\n",
    "of this model, we need to calculate some physical quantities of\n",
    "interest, including the mean energy $\\langle E \\rangle$, the mean\n",
    "magnetization $\\langle M \\rangle$, the heat capacity $C$, and the\n",
    "magnetic susceptibility $\\chi$.\n",
    "\n",
    "The Ising model\n",
    "---------------\n",
    "\n",
    "Consider a lattice with $N$ sites, where each site $i$ can assume two\n",
    "possible states $s_i=+1,-1$, or spin “up” and spin “down”. A particular\n",
    "configuration or microstate of the lattice is specified by the set of\n",
    "variables $\\{s_1,s_2,...s_N\\}$ for all lattice sites.\n",
    "\n",
    "Now we need to know the dependence of the energy $E$ of a given\n",
    "microstate, according to the configuration of spins. The total energy in\n",
    "the presence of a uniform magnetic field is given by the “Ising model”:\n",
    "$$E=-J\\sum_{\\langle ij \\rangle}s_is_j-h\\sum_{i=1}^Ns_i,\n",
    "$$ where the first summation is over all nearest neighbor\n",
    "pairs and the second summation is over all the spins of the lattice. The\n",
    "“exchange constant” $J$ is a measure of the strength of the interaction\n",
    "between nearest neighbor spins. If $J>0$, the states with the spins\n",
    "aligned $\\uparrow \\uparrow$ and $\\downarrow \\downarrow$ are\n",
    "energetically favored, while for $J<0$ the configurations with the spins\n",
    "antiparallel $\\uparrow \\downarrow$ and $\\downarrow \\uparrow$ are the ones\n",
    "that are preferred. In the first case, we expect that the state with\n",
    "lower energy is “ferromagnetic”, while in the second case, we expect it\n",
    "to be “antiferromagnetic”. If we subject the system to a uniform\n",
    "magnetic field $h$ directed upward, the spins $\\uparrow$ and\n",
    "$\\downarrow$ possess and additional energy $-h$ and $+h$ respectively.\n",
    "Note that we chose the units of $h$ such that the magnetic moment per\n",
    "spin is unity.\n",
    "\n",
    "Instead of obeying Newton’s laws, the dynamics of the Ising model\n",
    "corresponds to “spin flip” processes: a spin is chosen randomly, and the\n",
    "trial change corresponds to a flip of the spin $\\uparrow \\rightarrow\n",
    "\\downarrow$ or $\\downarrow \\rightarrow \\uparrow$.\n",
    "\n",
    "\n",
    "### Physical quantities\n",
    "\n",
    "The net magnetic moment or \"magnetization\" $M$ is given by\n",
    "$$M=\\sum_{i=1}^N s_i.\n",
    "$$ Usually we are interested in the average\n",
    "$\\langle M \\rangle$ and the fluctuations\n",
    "$\\langle M^2 \\rangle - \\langle M \\rangle ^2$ as a function of the\n",
    "temperature of the system and the applied magnetic field. \n",
    "Notice that in the absence of a magnetic field, the value of $M$ should average zero.\n",
    "This is because the system is as likely to be found with all the spins pointing up or down.\n",
    "Therefore, one typically measures $m=\\sqrt{M^2}$ or $m=|M|$, which is always a positive quantity.\n",
    "\n",
    "### The heat capacity\n",
    "\n",
    "One way to measure the heat capacity at constant external field id from\n",
    "the definition: $$C=\\frac{\\partial \\langle E \\rangle}{\\partial T}.$$\n",
    "Another way is to use the statistical fluctuations for the total energy\n",
    "in the canonical ensemble:\n",
    "$$C=\\frac{1}{(k_BT)^2}\\left( \\langle E^2 \\rangle - \\langle E \\rangle ^2\n",
    "\\right).$$\n",
    "\n",
    "### The magnetic susceptibility\n",
    "\n",
    "The magnetic susceptibility $\\chi$ is an example of a “response function\n",
    "”, since it measures the ability of a spin to “respond” or flip with a\n",
    "change in the external magnetic field. The zero isothermal magnetic\n",
    "susceptibility is defined by the thermodynamic derivative\n",
    "$$\\chi=\\lim _{H \\rightarrow 0} \\frac{\\partial \\langle M \\rangle}{\\partial H}.$$\n",
    "The zero field susceptibility can be related to the magnetization\n",
    "fluctuations in the system:\n",
    "$$\\chi=\\frac{1}{k_BT} \\left( \\langle M^2 \\rangle - \\langle M \\rangle ^2\n",
    "\\right),$$ where $\\langle M^2 \\rangle$ and $\\langle M \\rangle ^2$ are\n",
    "zero field values.\n",
    "\n",
    "Metropolis algorithm\n",
    "--------------------\n",
    "\n",
    "### Moves\n",
    "\n",
    "One typically picks a random spin and it is flipped or not by calculating the energy difference between the considered spin and its 4 nearest neighbors using the formula:\n",
    "\n",
    " $$U = J  spin(x,y)  [spin(x+1,y)   + spin(x-1,y)    + spin(x,y+1)+ spin(x,y-1)]$$\n",
    "\n",
    "The energy change is $\\Delta U = 2U$.\n",
    "The spin then directly flips if $\\Delta U \\le 0$. Otherwise, it only flips if a randomly chosen number between 0 or 1 is smaller than the Boltzmann factor $\\exp(-kT\\Delta U)$. \n",
    "\n",
    "Notice that the sum in brackets can run from -4 to +4, so we can easily store the values for all the possible configurations in lookup tables.\n",
    "\n",
    "### Boundary conditions\n",
    "\n",
    "Since we are interested in the properties of an infinite system, we have\n",
    "to consider the boundary conditions. The simplest case corresponds to\n",
    "“free boundary condition”. In a 1D chain, the spins at sites $1$ and $N$ are open\n",
    "ends and have one interaction each. In general a better choice is\n",
    "periodic boundary conditions, where sites 1 and $N$ interact with each\n",
    "other closing a loop. In this situation, the chain has the topology of a\n",
    "ring, and all the spins have the same number of interactions. We also\n",
    "say that there is translational invariance, since the origin can be\n",
    "picked arbitrarily.\n",
    "\n",
    "As discussed earlier, the use of PBC minimizes the finite size effects.\n",
    "However, a disadvantage is that they reduce the minimum separation\n",
    "between two spins to half the length of the system. In a 2D system we need to\n",
    "account for the periodicity on both the $x$ and $y$ directions, and our\n",
    "system will have the topology of a torus.\n",
    "\n",
    "### Initial conditions and equilibration\n",
    "\n",
    "We can pick a random initial configuration. However, as we shall see, in\n",
    "some simulations the equilibration process can account for a substantial\n",
    "fraction of the total computer time. The most practical choice of an\n",
    "initial condition is an “equilibrium” configuration of a previous run\n",
    "which is at a temperature close to the desired temperature.\n",
    "\n",
    "### Tricks\n",
    "\n",
    "It is convenient that we store all the transition probabilities in\n",
    "lookup tables, so we do not have to calculate them at each step. Another\n",
    "trick consists of storing all the positions of the spins and their\n",
    "neighbors to avoid calculating many random numbers. If you need to\n",
    "perform several runs for different values of the temperature $T$, you\n",
    "can do it at the same time using the same random numbers.\n",
    "\n",
    "### Exercise 11.2: Equilibration of the 2D Ising model \n",
    "\n",
    "1.  Run your simulation with $L=8$ and $T=2$ and choose the initial\n",
    "    spins to be all up. Plot the variation of the energy and the\n",
    "    magnetization with time. How much time is necessary for the system\n",
    "    to reach equilibrium?\n",
    "\n",
    "2.  Visually inspect several “equilibrium” configurations. Is the system\n",
    "    ordered or disordered?\n",
    "\n",
    "3.  Run the program with $T=1.5$ and chose the same initial\n",
    "    configuration with all the spins up. How long does it take for the\n",
    "    system to reach equilibrium?\n",
    "\n",
    "4.  Visually inspect several equilibrium configurations with $T=1.5$.\n",
    "    Are they more or less ordered than those in part 2?\n",
    "\n",
    "5.  Is the acceptance ratio and increasing or decreasing function of\n",
    "    $T$? Does the Metropolis algorithm become more or less efficient at\n",
    "    low temperatures?\n",
    "\n"
   ]
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   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from matplotlib import pyplot\n",
    "import matplotlib.animation as animation\n",
    "\n",
    "class BoundaryCondition:\n",
    "    RBC, PBC = range(2)\n",
    "    \n",
    "class Direction:\n",
    "    RIGHT, TOP, LEFT, BOTTOM = range(4)\n",
    "    \n",
    "class Ising(object):\n",
    "    \n",
    "    def __init__ (self, L, J, T):\n",
    "      \n",
    "        self.L = L\n",
    "        self.N = L*L\n",
    "        self.TWOJ = 2.*J\n",
    "        self.T = T\n",
    "        self.beta = 1./T\n",
    "        \n",
    "        # Initialize site positions\n",
    "        # Initialize neighbors table for boundary conditions\n",
    "        self.nn = np.zeros(shape=(self.N,4), dtype=np.int16)\n",
    "        self.position = np.zeros(shape=(L,L), dtype=np.int16)\n",
    "        self.x = np.zeros(self.N, dtype=np.int16)\n",
    "        self.y = np.zeros(self.N, dtype=np.int16)\n",
    "\n",
    "        # Periodic boundary conditions\n",
    "        n = 0\n",
    "        for iy in range(L):\n",
    "            for ix in range(L):\n",
    "                self.position[iy,ix] = n\n",
    "                self.x[n] = ix\n",
    "                self.y[n] = iy\n",
    "                self.nn[n,Direction.LEFT] = n-1\n",
    "                self.nn[n,Direction.RIGHT] = n+1\n",
    "                self.nn[n,Direction.TOP] = n+L\n",
    "                self.nn[n,Direction.BOTTOM] = n-L\n",
    "                if(ix == 0):\n",
    "                    self.nn[n,Direction.LEFT] = n+L-1\n",
    "                if(ix == L-1):\n",
    "                    self.nn[n,Direction.RIGHT] = n-(L-1)\n",
    "                if(iy == 0):\n",
    "                    self.nn[n, Direction.BOTTOM] = n+(L-1)*L\n",
    "                if(iy == L-1):\n",
    "                    self.nn[n, Direction.TOP] = n-(L-1)*L\n",
    "                n += 1\n",
    "\n",
    "        # Initialize spins\n",
    "        r = np.random.random(self.N)*2-1\n",
    "        self.spin = np.ones(self.N, dtype=np.int16)\n",
    "        for i in range(self.N):\n",
    "            if(r[i] < 0):\n",
    "                self.spin[i] *= -1\n",
    "                \n",
    "        self.Mtot = np.sum(self.spin)\n",
    "        self.E = 0.\n",
    "        for i in range(self.N):\n",
    "            self.E += -J*self.spin[i]*(self.spin[self.nn[i,Direction.RIGHT]]+self.spin[self.nn[i,Direction.TOP]])\n",
    "\n",
    "        # Transition probabilities\n",
    "        self.de = np.zeros(shape=(3,9))\n",
    "        self.w = np.zeros(shape=(3,9))\n",
    "        self.set_temp(self.T)\n",
    "                                                             \n",
    "    def set_temp(self, T):\n",
    "        self.T = T\n",
    "        self.beta = 1./T\n",
    "        # Lookup tables for transition probabilities\n",
    "        for i in range(-4,5):\n",
    "            self.de[0,i+4] = -self.TWOJ*i\n",
    "            self.de[2,i+4] = self.TWOJ*i\n",
    "            p = np.exp(-self.beta*self.de[0,i+4])\n",
    "            self.w[0,i+4] = min(p, 1.)\n",
    "            self.w[2,i+4] = min(1./p,1.)\n",
    "                                                             \n",
    "    def metropolis(self):\n",
    "        nchanges = 0\n",
    "        for n in range(self.N):\n",
    "            # trial spin change\n",
    "            # pick a random particle\n",
    "            i = int(np.random.random()*self.N)\n",
    "\n",
    "            # change in energy\n",
    "            iright = self.nn[i, Direction.LEFT]\n",
    "            ileft = self.nn[i, Direction.RIGHT]\n",
    "            itop = self.nn[i, Direction.TOP]\n",
    "            ibottom = self.nn[i, Direction.BOTTOM]\n",
    "\n",
    "            spin_sum = self.spin[ileft] + self.spin[iright] + self.spin[itop] + self.spin[ibottom]\n",
    "\n",
    "            s = self.spin[i]\n",
    "            deltaE = self.de[s+1,spin_sum+4]\n",
    "\n",
    "            if(deltaE <= 0. or np.random.random() < self.w[s+1,spin_sum+4]):\n",
    "                self.spin[i] *= -1\n",
    "                self.Mtot += 2*(-s)\n",
    "                self.E += deltaE\n",
    "                nchanges += 1\n",
    "        return nchanges\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T =  3\n",
      "<E>/N =  -0.82472\n",
      "<E^2>/N =  0.7169248\n",
      "<M>/N =  0.2751\n",
      "<M^2>/N =  0.10981480000000002\n",
      "C= 0.0040846357333333356\n",
      "chi= 0.011378263333333338\n",
      "Acceptance ratio =  0.45854333333333336\n"
     ]
    },
    {
     "data": {
      "image/png": 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Q1TnnACefDPztb63nYpNNgCFDZJ2NIylUtfrq7hu0lVZqfH755cbnXXZpLmfrHFeiE0JHhKqIaCoRzbK89tDLCSEEANtl2QvAGAAnANgCwFoAvuXanhBishBitBBi9NChQ1Pb7UoddDUcLk9EDTyXNMSzPkhc3HbS4BIOc3nWQfL0yqp7aT6oxta2vrI6x33K+5wXda579pTPB5j4DH8e1zkeF4JT9sU11iZ6/5w6Dy7hAOw3Tz7puEm26OnselnlzT/7rP1/ScKh5vA2PSGFHmZ2Hfek73HnRB+sM+ka41BVhBBinOs3InqLiIYLIeYR0XDY+y7mApgphPhX9J+bAGwN4JJCDI7ISzgUSWmMZsXLUzh8+1lcGTh1yaoKLZckBOYFlpdw6GMzhTy7oBPXv2OeT9v5TTt5lyof53H49h0p280HAV28/37rf4D4sJ253CYcPqNAhPZppI0IhKTjcue4m1sAqGDQBAA3W8o8AWB5IlLuw04AnivasLyFIzRPPM/hI3w9jjyFI0vFzStUldTAmbHjtMLhugnIIhxxjaW5X7aB/UI6pG19BKHC4TPIYZItehqzXjZp9N+kDMKQ4YP0ybFc2/Bdl424//FzHP5MArAzEb0IYFz0HUQ0moguBoCoL+MEAPcS0TMACMAfizbMdQLTCkdSHnieHoevCJnLXSmYcbbYLvC8KPoBQPOcpREOIYoVDp9QVVyZ0H1S5V11IY1w+IqYSziq9jiEKMfjANpPOCrpHBdCvAPgC5blMwBM1L7fA+CzZrkiqdrjyCIcZpqfb6gqzTazTnTlQ1F9HIsXy45R3/KuMi7h6Nkze6jKtj2zv8xWRi3zGR3AJhxxfRyhwuEbqtL7TrJ4HKbopfE44oTDJiS+hHgcPFZVG5IkHO++C+y+e2P5xRfby/uOXGq7i5w6tblhA4A//xk44ww5B/nhh8tlv/mNHEBNYTYWtm3vvrucQjapHBAvKK6npOMq7htv2Jc//rh9e65Q1WuvAbvuCuy2m5xzWmVomf9Tn7/xjebfFy+W2XAbbiizdpLEHwDuuqt5xjmVjaajexy2O8gkgZ48Gdhzz0bZ3/2uOUPtl79sLq/v51lnNW9DTXkcR4hwxHkclzh6HVX5/feXY2v99a/A6ae3ltPr0pgxwDrryHq6xx7Ndk6a1LytuGeWzjvPLRx62W9+U75feSVw553NZZcubS67zz7Ac1qwPCQHp6xQVVnwnOMGSSfwz3/2m7j+kEPke5pQlUqR1DnooObvF17YSIlU8yubwmGrrDbb0wiH7nGYDfvAgXZh+dGP7OvaeWc53afpYbi2f9JJsiEHZKqlib7fb77ZGKBP8fHHcnTT5wJ7zPT13H+/nPPatt20oarDDmt87uqS83brmMdUP29qMMK0qHW57I4TjokTW5fr6+zqAg48EJg9W34/88zmcp9+2nyuX365OX1VreeUU5r/ZwqHfu0eeyxw4onyc9JI14rx4xv/UevUj/GUKfL5D4Xr4V8bIaEq7hxvQ5I8Dl9XtW/f5v+Z61H4hB9s2C5iH4/DRhrhcP1GJJ8ZsJEU3vINoSXdWSV1mprxcB+Pw4YrNJilj0Phc/eY5ygDSWHBNFlVun1xN2ShoUjb8pA+jrgUeb0umB4HkH4olzJCVSwcFZIkHFkuHn25wmzsfd1NWww7b+GII85O14WZFHf3DVVVJRxJ3mKScISEEnzOSdbJxmyhnrgGPm3neFK5JHxubEKyqnyFw/Q4gPTC4ZMinhUWjgrJy+PQ3fQ4bI29z8n3EQ7fhiVvjyOtcPgmCoQIh61sXh6HSzh69rQ3wCECnbbDPi3K9lCPowzhcJ1v8wbB3IZrGugqhCPpWkx6UNgHFo4KyUs4bA802b7bhCMus8X1P9e6fEjTQLvScdMIh+tJcVf4JA/h0Bv2vIUjD4+j7FBV0cKRpfPX1+NwhapCnsUwQ1XmeejfP95WF0kPAGb1HgEWjkpxHXiXELhweRzq/4sWyWEezDi5EPHCoS5A2wib5rKsoSo9i8hEPw7m9Jqui8CVVUUkh2dQaZnvvCMHSjRj8K+80vyUsQu1/bfftk+h+t57zUOdxO2nTlKoSg0x4RKOkIbeZ+rXRYv812dDHxZFFz0XvsJhu8mKa9CI4o+Nr8dhokQgxOPQExDy9DgWLoz/Xb82Qhr/hQsbN2QsHBWSdPcdehfvEo7llgNGjbJ7CXHzOagGSf+fEgyz8zlrqMo2l7pCP07mNKWuC1MfzE7n3XeBYcOAHXaQ3994A1htteY+jnPOkSPIDhrk53E8+aRc53bbtf6+666NKVazYB7f739fvvfoYb+AQ4RjzpzkMiFza9vQs/fK9DjM82fLjHOtR0dfz6ef2gc5BPIVDpX0EsoJJ7h/I5Ip+GkYPLg5bZmFoyKSKmnWPg69sr/6qv33OI/DJhzqwohL1/Sx1UZoGCsuVBXC0qUNQezdG7jjjuRtK7q6mtMm8yLJ41C4ZnzLs08ib5I8jjThFJfHYR4bfdoBGz518MMP40VPJ65+6l67LauqCIiyNfhKeFk4KiQv4fANbeUhHGodZqw+q8cR91uarCobK1jnfpSofezdO77hMenqKudhKNfxNSfuUZT5gFYoZXocoY2x63zqy95/Px/h0PfR5nEUJST6Ne/b+Nv6T1k4KiKvUJWPx2H7ntQ5HudxpBmDSf+/jTQd5yHC0b+/e3914fDdNlDcnaKvx+ESDt+ssSpIEg69jI5v+SzCIYS9T09fT9x873kKRx6d2CZJfTwuQs9HnrBwGOTtcSQ1FkV5HCGVMe5iCPU4QkNV/fq5B9ZT+2j2Gfh4HGWEGLIKR51CV2Wm46bxOGwZefp6PvjAv9H0FQ7bDUhR5yzNTUTaZ8DygIccMUiqGKEeR5KHYfsed4ftKxw9e/rfHVXtcbjW5coWCQ3/5UWS6Ct8Q1V59AXlRVrhsGEL02b1OGzCodsTF6oyt1e3UNUnn7jT2+OwCUdHj45bZ1yN0v/8j5ypzPdiV+t57LH49dsqpikc993X+GwTjmOOAY4/HrhZm9Xk00/9MzXi9umWW1qXPfGEOxPGNhaWEMDZZ9vL9+vnHopE30f9grjtNnt5he9DlKHcbMwaE9c5bmtgzEER6yQcDz0k5x2PEw5bXbCVnztXDs7oClX5ZIzpuDyOm25qfI4TjltvldO19ugh6+fee7u3tXSpzGr8+GP5+dprW23Jm/ffT/ewpH5M7rxTXmd5DJboAwuHgatiLF4sB2fbdNOw9ajRN13YPA4zdDNOm0tRVSo95vuXv8hB7sxB13xd17gGbL/9Wpfpc6j78PDDcu5nG337+nkcIRQlHNOmNX8PDVWpUY0VVQiH61j+6Edy5Nq4hscm2LbjfOml8eU23zzeRhMhkqfdXbLEfc6ffVaK4iqryGdXRo1yr2fpUnnj9vHHsh49+mjr73mz1lrAM8+E/08XjvHjge235z6Oyki6o7B10tnwDfHYPA6fOQ7M9cyfL/+7777Aj3/sZ6OiiIth1VUbn3WPYvnlm8vF9eekfbBp6dJi9sm2HRtEfmJXJ+FQ+GYmJS03yfrkuM/T/Um2qAce4wbbVMKhtmtSRD+C+dxWO4SqWDgMkiqG7wXg26mc9N31f3P9H30kK32aSYSKaMCWXbbxWd8n8yJxdYwD2TyOOnaOm3SCcPiSdayqtMPC2IgbM00Xjrg53fMkbT1g4agRSQ2Or3AU7XHECUfo3V0RDdgyyzQ+xwmHr8cRQtXPcbSzxxH3AGDIct/1+uArHL62xHkceh+jrS1g4ZBwH4dB2cLh+2yAWd4mHL16pROOIi6GAQMan/V9NIUizuPQw4IhF0RZaa5xU/PWVTiSjk3SWG2+5U3qEKpS+HocZYSqbNlqHKpqQ4oOVZnYRlhN43EsWVKvUJVuQ5zHEWerujMMvVjLGiqiHYUjbf1O6pxOImuoKu4Bv1CShEPV0TJCVb16tdYD2zZs5802QCoLRwXst19ryqWJr3Bcd53McjAxK8BppzV/tw3WZvv/Pvs0L69bqErfh113bXw2hSPOViUcF18M3H23/7ar7uO47jrgK19J/n/exz1pn/ffP73H4Zr2ty4eR0ijecYZ7t+S+jjyrlc9e7bWgxtuaC23007N319/Hdh22+ZlLBwVcd11yWWSpj/Vefjh1mVJd6O+Hofrv3XxOFzHyQxVxTUovhlsJmX1cWTdRtnCcc016TvHFWPGhJUPLefC51jl0WguXdoYAdcmHLY6mZRybzJoUOOzzeOwMX1683fbwJAsHDUma3aHEPHurm8fh0mPHnaPQ++kTrvNNOjzXeiECEfahrUsj8NHOOKeeclbOMzzqFKfR45sLHMdF3VekvbpoIOav5clHGX2Wymv2HZ+zBuiESPCbiaB5mejfIXDJDSJIW9YOALJIy0wrqFOqkSuC1sNMZJGOIrwOFzCERKqSitoZQlH1m0U7XGo77pYu+qPa4gcEzOZoYxQVdpBANMgRMPj8BEOInddd6FHBHr1SlfPs84wmZXKhIOIBhPRPUT0YvRuHWCbiM4momeJaDYR/ZaoLE21U4bHkSZUpQuHXqmqEg5XZ2oZwrF0aTkdz1k9tbw9PXPYCvVdP+auoS2ULXUUDsBPOPJqOONCVWa97tEjPHFAPxZ5C0d38DhOBnCvEGIkgHuj700Q0bYAtgPwWQAbAdgCwA5lGmmipjdNS1GhKpfHocdT024zDVWHqtL2j4SQ9bgVGapyCYdef8zZ7IRIbqDj0qfjKDpU5ZvJ5kOZHoetc9wH23XTXYRjDwBXRJ+vALCnpYwA0A9AHwB9AfQG8FYp1hXETTfJObVd+GZVmWQJVf3pT8llQqkyVDVnDvDzn6f7bwgLFiSXcZ2vW24BnnsuX3t8PA69U9UUjrlzwz2OpCxERTt6HFdf3fqbmlde0aNHuHCYHkca4bB5HCFDy2elSuEYJoSYF32eD2CYWUAI8SiAaQDmRa+7hBCzbSsjokOJaAYRzVjgc0VXxKmnAmuu6f49KVTlwhWqGjo0+b+vvRa+vSRccyz369f8vQiP48Yby433xuESvz32AA45JN9tmcKhjp8uHLvs0vhsCseoUeHC8ZbnbVyWBs23jyNv4bj88uSyRK2DVyZRVKhqzpwOEQ4imkpEsyyvPfRyQggB6V2Y/18HwAYAVgOwKoCdiGiMWS5ax2QhxGghxOihPq2lB2UNUayTt8fRvz8wdmy+Nvpw6qnAKae0LjcHOSxCOOpEGYMt2ralC4cp1grT+1u8OLnxda2rCPTGsYpQlWKttdxliYCJE4GFC/3Xb3aO5+VxKHvKoNAhR4QQ41y/EdFbRDRcCDGPiIYDeNtSbC8AjwkhFkf/uRPANgAeLMRgg+WWC6sQebB0aXxjGpeOq8bj1//vO+BeWYQIR5mNblGUuQ+ujm+zIYxbXpRwpKmDah98PI4ihSPuuShVf0MabL3O9+wZ/yS7i6qFo8pQ1S0AJkSfJwCwRUtfB7ADEfUiot6QHePWUFUR6CO8lkXaUJW6sMxQlWtSoaowj2mnC0eZx94lHK7GvkzhSHMuQ6abrUo4dHHzpahQVagdWahSOCYB2JmIXgQwLvoOIhpNRBdHZa4H8DKAZwD8E8A/hRC3lmWgT8dy3qR9jkP9zwxVVelx2CpxiHBwqCr9tuomHGkEtB2EI43HkUeoquoHAL1CVUR0I4BLANwphMjlHkoI8Q6AL1iWzwAwMfq8FMBheWwvDT6prHmT1uPQhcP0OOoUqjLFmIVDksc5qrPHUbRw5DnMTNkeR5p6nnW04qz4ehwXADgQwItENImI1ivQptowcGD520zbOf7f/8r3rq76eBy2RmYF4zHPOOGYN8/9W7vQv79fuTxCWqEex+DBrcv0ebxtuPpLksgSqiq7j8NMGohbb9Y+jsWLW1N8XYwZ03g+yWXTK6/425EFL+EQQkwVQnwdwOcAvApgKhE9QkTfjvoeOorVVwd+97v4SYZcjB0LbLZZ+m1nGeQQkBWnLsJx/PGtyzbZBPjiFxvfq8hcK5OLLvIrl4dwuNZha+w32QS47LLwbYQIx3nnNT6nuauO8zjOP7/5e57Csc02zd/jzk0aj0P3YPRneWxZiDpK+oJGAAAgAElEQVQPPdQQBte+/uMf/nZkwfuyJaIVAXwLMoz0DwDnQQrJPYVYVgETJ8r3jTcGjj46nds3aZLMxkpL2j4OxUcfNVdM39noimDAAOAXv2he1rdv81DyeQmHTaRCCB1R2JeVVvIrV3ao6vjj/W3TMe/GFfrAfYpjjml8NjOHQvsP9X1bfnkpfDp51vG1127+HldHs3ocOubzXbbnvVT7UHX42bePYwqA9QD8GcCXtQf3riGiGUUZVzbq5KepDAozHTaUrMKxZEnz9vO8E0uD2dD06dPqEeVB1thunz7hTwD74GtXkaEqW2OfdugQl3Ak7acpHD7evMvj6NGjVeiLDFXF7VvWPo647djWqdqHqjMlfavPb4UQ02w/CCFG52hPpeQhHD17ZmvEkvo4kipMknCU7YHYhEPfv7yEI+t6evduf+FweRw2b6qdhMPs47DNOVNk53jeHodue9++jfGvfOpwUh9HWfhWnxWIaG9j2bsAnhFCeHbt1B/z7iFNY5RmBj6dJI/DRzjMaVv1Sqbm7SiLdvI4iiDrHPUhuITDZkOccPTp434ozdXgl+lx2K6xIj2OuHOYR1aVEo4Qj6NdhONgyCe2ldexI4AnAaxJRGcKIf5cgG2lk1eoqkiPw6ePI87jUEOTlIV5EfbuXYzHkVU40iRC+OBrVx7nRB/yP4tw9O7tFg5XX1DSeczT46hTqCrPPo52Eg7fy7Y3gA2EEPsIIfYBMApybKmtAJxUlHFlEyIcG28MbLBB6/KhQ4sVDhv6RbTjjvEeR5rhDbJgG0Zd37+88s6T1qNnctlIG7pJwnf/8nhmRR/AcM89G9l9Nht8HmoLgag1GwlopLSb9c7neCu7zeHebaGqPIUjZM6RrFlVZhg5ibqEqnyryGpCCH0czLcBrC6E+A+AEmY+KAffUNWllwKPPQY88EDz8l/9Chg2zF4BfNMyQ4XjkEOAo45qfD/pJL/O8aSGNISnn5bPkcy2DAajLsI11wT+9S/5OY9Q1aOPNj8jkbSeKVOA+fOB66+3/15UqCrpXH7nO/J90aLs23rvPfl+4YXAH/8o0zfffjvc4+jRQz5DM2CA/feddmpdRgTcey9w//3Ny+fNA7761XTCoWN6HEWGqsx1l5VVZS736RxfYw3/7eaJ72U7nYhuI6IJRKTGlZpORAMB/Lc488rF1+MYNkxeVEOGNC9fbTX5bqvA6rc40vQ/jBjRbGevXn7CYaYzxpH0BP2IETIF2Xy4T9kDSE9MpRfmEapaZZVmbybpwu3XT563VVe1/16VcKi01KzCoR/HwYPlsRkwQB73UOEgAlZe2Z4OCsjjaPtP//7A8OHNy5dZRpY3J9byCVXpdpfpcZjnzKePIwQzXd61LvV99dUby8xQVRWjWwD+fRxHAdgbwPbR9z8BuCEaDn1sEYZVgW+neFJlSZsho2YDC6mMRM32ErW6wjZ7fBps1UlqznrmWpfNbtVAmR30IXa4tunqDLaRdG6rEg613XffzbYd/fia2WGhwpFlJFvbtmyd7SF9HLZ+OnM7eWZVueywUUYfh349m1P8ljXEiEmicBBRTwBThRBjAdxQvEnV4RuqSmrsbBXY5wT37Bk+5SlR6x28eadms8fngbf+/eUFn2STj3CEZPz4YOsw9cFVrqrO8XYUjrj6batXWYWjq6vcznGTIrOq4pbbjmnb9HFEAw12EVGG56HbA99QVdJy2x2+r3AAYeGqJUta3V1b/NfEp6F1xbhN4i4em3Dk4XGYz6P4Xrh18zhUA5pVOHTyEo6QxinU4/A57y7hKDpUZVLkcxxxddgmHOo4Vi0cvqGqxQCeIaJ7ALyvFgohjnH/pf3wFY4iPQ4gLMPGnGfYFqpKKxyhgzyW6XGEhqqSttfuHofOBx8k21CUx+ESDvM/IefdJhw+N0d54ZNVFUJoqEovbwpHVaEq39N3I4AfAngA8vkN9epIfOPlOtttB+y6q/ycVjhUBQnxON5/Pz7E5gpV+Vy4o0cD48a1jjels/LKjSdt4+5s9Qtfv7vX/xOS6eUTqrLNez5qVOPzRhsBhx0mU5h/+1uZwrrFFv42+Nr5k5+4G2p1LMzG3sXmmyeXOfjg5u9lehy+T6nH1b9ttgGuuAK4IQqMr7BCqxdfN4/D5Kc/ldmXIf/xCVWpeqKOR62FQwhxBYBrIadxvUK9ijWtfMyGN26aVpOHHmoduO2ss8K2nyZUpXscyi6fuzGfPo5+/YB77olvrG65JTxUpWeC6LZeckmyTQqfUNUBB7Qu69OnkQJ79NEydXXaNOCzn5Upu3//u78NvnaedlrzwI46ytPxfb7mggvif1955dasp7yFI9TjsC2La/AuuAA46CBghx3ksynmTYIQ4UOOHHigfP/Vr9xlXMSl57r24wc/AL79bftvWUJV77/f+r8q8BIOIvoygJkA/hZ935SIbinSsCowK78rO8pX5fXnDMoIVdka8CyhKp8ss6SH+UKEI7SDMSlU5VqfEuaiHvqz2eCyRXkcvsKRV5i0zKwq2/ZD6pSZGShE+HMcvhmTSfaY60izvixZVWp0gHYJVf0YwJaIntkQQswEsFZBNlVGFo/DRlrhyOpx6LguKB+Poyjh0PtO0gpH2qwq3ZY6CIfyOJJSns31uchDOJKIa6Bt9SrU40gSjq6u8FBVmuwnRRqPI2R9Scvb1uMA8IkQwuy+q3hg3/wxK1dWjyPkATUgncdh6+PI2+PwmTrT/KywCYe+vizCEfc9DmVLUXNw6LjCh4pQjyMJ3wYl7z4OdUx9Q1W+NyM9elTvccQJR5r1uepdO3kcvvcdzxLRgQB6EtFIAMcAeKQ4s6rBN1TlW1lCG6Y0neNJHkeW5zhMu2wkZUjZhMO17iy58Lb/uhoSdXzTZnSF4Buq8vU4fKZQ9SHvrKo4MQ4NVZl1wsyqyuJx5B2qyupx+PRx6OWVcLRF5ziA7wLYEMASAFcBWATg2KKMqgrfUJXvyVKVe+WV/S7oNB7HOuvEexyAzB4yycvjSLqIihKOuItZseyy9v+uvLJ8d80Hrn73JW7YB99Qla/HkTRznu8zRHHnNI3Hocqq/dHtzDtUZescX7JEzr6ZtM68Q1Xrrpttffo0066bIf0BXNPjqArfrKoPhBA/EEJsIYQYHX3+qGjjyibvUFXPnsDjjwMzZ/qdaLVevaxtQDn9orzwwlbBM0NVl1/emhlVZec4IOdGfu21eI/lM58BXn7ZnqabFKqaOlWKqo3TTpPpnip92mTmzNZlf/qTvSwQP21t0jH0FY7+/WWG2/rrywE2r79eZvKZ+PZxxD3wmCarSp3ffv2AW29tts0nVHXHHXZ7fTvHXVx5JTBrVvx5eOGFePGPE46f/zx++y+91LpMF73bb298Ns+TOs7vv99YlhSq0ucwLxLfrKp1iWgyEd1NRPepV9HGlU1SqEoNNhYSqtpyS5keGTJ+lR6qUgMH6gPObb11w56BA+Pvprq65EUxblyrbb5kEQ61HXP/N91UjuwZ9/8ddgDWWgv4/OeTbTL/+4UvuG1ecUWZ7unyOGyD+MU935E0YKDNPoVvqKqrq3EOt9oK2Gcf+eyQie+dqI9whKD/Z/fdZXqzwsfj2Gor+2++neMu1lkH2HBDt3Cssw4wciTwpS+51xHn3SaNOLD22q31Q///Cis0RMvcji38l+Rx6AMiFolvH8d1AC4EcDGAEqcBKpekUFXo8AKufO0kbCKjr0vdpap1mnaZHodeRlFW53hIarPrAvVpeIqO9frEz+N+c5VRjUqSx+HbB5KnxxHye9yNkU8fh6se+IaqXCTVe5+wXJprJ8Qml6jZhCMpq6qMhA/Av4/jUyHEH4QQfxdCPKleaTdKRPsS0bNE1EVEzjnLiWhXInqeiF4iopPTbs/frub3PDvHQzwO8yIxt2kOj5GUVWXaYpZx4ROqSnoIryzhKJrQhtH8LSnVslOyqmz4hKpc9cA3qypp21ka+7yFw3UtujwOW+e4K1RVN+G4lYiOJKLhRDRYvTJsdxbkMO0PuApEo/L+HsBukDMOHkBEo1zl8yTvznEgfajKti5zqHKfu++ihEMnroHPWzjKyIjSSdsZmeRxqPPi61Ek4Wtn3PnP2+PI2jluy6oKrZO2/kNf8vZuXaLpEg6dpKyqsoTDN1Q1IXo/UVsmkPIhQCHEbACg+DOwJYCXhBD/ispeDWAPAIV1/yT1cYQ2pKGhKlsjG+dxmMKRd6hK4ZOBY27X3I6PcPi68K5tFUlRoaoyPI7QY5WmcU3rkdnK+ISqfHGFpszvIaGqrIR6HLpt8+cD06dnfzg5K75ZVWtaXqlEI4BVAfyv9n1utMwKER1KRDOIaMaCBQtSbdA8gWV4HHrqZ1wl1kdPTfI49A6yQw5ptQVIn1UVN5Oh7biozv0f/zj5P0SNMYX07dZBOMyZA1XH+s47lyMcrswtfdrgJBtsbL89MHas/TezHqrMvDw8DnMdScKhe+FphMN1TftcB336yBknfTnjDD+bFPp1tt56jeWuYzp2bFi0oQhiDxsRfV/7vK/xW+wQfkQ0lYhmWV57ZDPZjhBicpQqPHro0KGp1pHUOa7Iw+NYbz25bN484Oyzm3+z3V3pDUtSH8egQY0Honbe2W5zmlBVnz4NITLtc61TDal95JHx21Cf//IX4Pzzm7dbB+EYNAh4443G9wkT5H7dfXc5fRznnGNffv75wK9/3fge6nE8+CBwn5EfaXq0ihkz3OupUjhcwqdv2yUcas6ZpGFU5s6Vd/qmfTZOPz3+97hQ1Zw5jeVxN5J1f45jf+3zKcZvjix4iRBinBBiI8vrZk/b3gCgJ5etFi0rjKRQlVkuCb2CmOuKG6DP1sehT87jClXFkcXjcKXUusqHYDYSqqHQbaxDHweRe67opP/FldeFI2182haazELSOFZ5ZFW5wsDmZ9U5XpTH4TNZmRCt5z8LrmvRp49Dt8n2n7JIuvzI8dn2PW+eADCSiNYkoj6QIlboiLy+wuHbaOkn1Uc44vo4dOFwhariKlGaznGF7oGZ/8vaUNkaDDObpA4eR5xw5BGqWrIk/cCDZQuHjSI9jq4uKRxJiRZx287icZjrykpoOq6Nug85Ihyfbd+9IaK9iGgugG0A3E5Ed0XLVyGiOwBACPEpgKMB3AVgNoBrhRDPpt2mn13N71n7OHRcnXK29dkqjD4MiStUFUceHkcR7rGtc9y8KOoiHHqD6iscSc/+lOFxhB6rpPOdRx+Hr4eih6rUhGFx15Jr21k8Dte60uLql/DpHFdUHapKurfYhIgWQXoX/aPPiL73S7tRIcQUAFMsy98EMF77fgeAO8xyRZHUgPtmVdlik3Eeh7m+JLc8KavKRh7puEVUYFsDbO5XHYQDSDeqb4jH0Z1CVXGNv3lTpQvHRx9VE6rS15UVl7fVTqGq2CoihCgpK7gemCdw+eXjy4VgVhaVbWRbX5IrnpRVZcMciydNVlXRHkdIqKpssvZxuI6dOpfz5mWzTWHLegutr2b98iFrqMoFkRyv7OWXgZVWksvMIWGyeBwqO87HHnX+hw8H3norubwL1w2pqx3Q2wpF1R5HDS7J+qFO4OWXA+ee2/p7UkNmqwhmZbn11tbyClUpnnmm8VnPvEoTqvrmN+WAbGq8I30fbr/dPoKuwnfIkTTEeRxpheP66xufH3sMuNk3HSOGtKGqpOOzlkdS+yMBExjYBmPUbdhmG+Bvf2stM2NGY6rjJOGwLY97gNEVqtIHQtRvbFxh3E03BU46Cbj44nh71lijddsu4VDhL8Vhh7Xaqth4Y7n9yZPdZXww2wKVUadE7OqrgX/+s1FOZRnqsHDUCPMOfuhQ4LjjWsulaSzNyqI/F2DLqtphh+bGfPDgxvhCaUJVvXoBJ5/cqJx62fHj7QPm+YTmquocj2OffRqft9oK+MpX0tunk6ZzPAnXvimBv/pq2djHoY7X0UcD224bX3bsWPtow5tvDuwbJdyn6RzXR3A1cXkcZp1TA3m6wrj9+smh07fcMt4WPfU7STjMfVXp66atgLz+Jk2KH/DSB9MGlfiixPNrX5ODRKrjsOKK7nXUtXO8W5GUqeDTQLvwefJYbzhtd99qmXlHmCaU4+qgsy0rMlRU11CV7fi4+jV86kORd4hxs++Z+NwEpOnjiBMO2/GJmzfE5XH49gHZEi5cuJ5ZKRJz35Vw6FMq6+Vs56PuWVXdkiJOhk8cVpXRhUO3SZVLE6oy7UiTVRW3vrSkzaoqmqSZ7MqyyefcJgmHr90qcy9NH0caj8NVLlQ44lJ7zZuPJI+jjIbY1R9k9kPGzarIHkeNKOOu0IatUyzE40hTeUL+U7bHkbWPIw+S7rrL8jjyEA6duJsAUzhc5OFxxKUNux6OzeJx+IaqbOTdLrjW5/I44oSjKlg4NHwb4jQnzUc44hojosayNH0cijQeR1l9HIo6hKqSGqm8+jiSqNLjCCFOOGykCVW5bPfxOFxl03hXWXG1BeYcKXHn9e6787UpFBYOjbR38KOMwd5VZ+yIEY1lm2zi/n9c/4Le0BcZqrI1hLZQlbmtkMHfbNhsV53B228v33Vb8+roTqKdhEOl4LqmyvUVDjXg5le/Kt9djalttrwDDoi30cR2HvfbT74PGdJYFjdsDyBn7zPt1P/jG6rabTf5vv768XYn4dNxvvbazVM5q22bfOMb8t3M/AKAG2+U7+PHt/5WBiwcGmmE4733gKeeal527LHAO++gabrXzTeXyz78sDGmvsJne7rHkWbIEUWSx/GznzXmUY7zOA47DPjPf2ROexZsNo8bJ4+Vyv7Rt3/99Y2RghcvBg4/PNv2Xeh33fff3/p7qFiE3tGGrH///eXc1ocemlw2TjiGD5fn9NRT5XeXzUccIc+PzkUX+dkKyGl7baP9nnGG3L4uHPpxMMdwW7xYpqybgmITDv1GbPHixvbVeT7kELlP5k2g+o8P771nnwde5513pNg98ogsD8h0cX30a8X55wMLF8bP1qjsLpuUo+N0JkmNqu1itk1yTyTTZ01sy1zbi+vjSDPIoWv9Jssv3ypstrvvIUPsDyblZYd+rPTj07t3Y/8HDpQpmkWg7/Nyy7X+7vvkeBkQybtYH5LCfj7n1Fa/fWYUVKy2mv2Y9ejRuv044VB9Aj4eh27LwIGN86vqkuuaDcHWFpiobfTp05xeb0YRAGmj6yFkRR52p4E9Do2qUtziQlX6d1M4zLIhHkdcWZ8hP/LC19sqG9fDfrZledrnkyadZZ0h57KouL/ZCRxHnHAoTI/DNjSMGapS/TllzZhXFJxVVQOK7ByPw6ePwydUlXWbCp8QWF7HwMf2qjvH8xCOIrOqQqjD8C1FC4fNGzSvp5BEgKozmOJg4agBeQ9mFkpSaqqyy5V7XmQDZrOxLKo4H1WHovLM00+T0lokPiEdRVbhcGVVsXBkg4VDIyStMU98Rn/Ny+NI+o8Q8WXK8LZMqn6OwxWPj/vdJGRQP991+tLOoSrdXpdwmHbaQlVZPI46U9VNLguHhquP46yzZDbPjTcC3/6238B0Iey3nxwnSGUz6aiLpWfPfPo4zP/Yvh95pEzJPPHExrLjjgOmTXP/X3HqqXLQxLR22LClIxaN6878xBOlzcce21gWctx32SX+9yKEQ0/3DGlobrsNOPjg/OwA5BhtewRMHq0fh08+sZe58srm7zaP48QTZZ0+4gj5/cwz5XWnUl7L4HvfS//fP/4R+MUvWpezx1EDXKGqU06RA+dtvDFw6aX5u/sDBgDXXts8JLaqEOpi6du39TmOLB5HHMstB1x3XfPgaueeC+y4Y/J6fvazsNxyH9tDQht54erjOPtseYORNpNlgw3CyufRMPTr1xjAMEQ4NtusdSTarFx7bWOgTR/0/ddnwdQxj6lNOFZcUdZplaU0bBhwzTV+dSsvz2vSpPT/nTjRLjwsHDWg6oHDbH0cSjj69HGHqvIY5LDo/2VZXxXCkRSq0mmHzvEq++/0fQ8NDfkIh4lrwq2qyXoubSm7LBw1oOqBw3yFI+6p7yTq1tFXV+EImbQpS4jQ9XvedbHqxA9FGcJRdWKDi6y21GUmTICFo4mQweKKwFbhdeFwdfTl0cdRFT52hHSm5kXeHocvRTzHAbSvcOj2phGOPCgz9TwU7hyvAXX0OFT2h+5xKIrKqiqTTvA4fAg9rkWNyFpFOm6VoSqmGFg4NKq+K7M1ULrHoQb/MxtSJS4ffZS8DZdwhDaOed+FxW0/bliRddeV7yNG5GOPQm98llkmvmyenp4a2HHTTeW7GngwL9rZ4/AZQHDAgOr30UTNdFjEDSmHqmpA1Z3jSaGqyy8HnngCWGkluUw13osWyXfb9K8mdXsAUK0v7bzmhx8OPPAAsNdewAsvAG++mY9dqoE755zkgRxN+266qbWM73G/+WY5aObPfw48/DAwerTf/5JQx7fqRjVUOFSH8LLLyoysJF55JX+PI+s1c8st8pzm8cyIngYOhGWo5UmbP/6SL3UMVenCMWCAbEjeeksuU/aquRDihm6P21aV+AhH0v/HjJGfR47Mxybdns0287NBR6WH2i7qpOO+zDKNbSbNHx6CarSqfApet8MXNRDgZpsle36AvKmqWhxNll3Wrx75sNFGjc/rrZfPOtNQs0NcLXUKVZnCoafimfYp4fDpRK5rVlXd4tLKHtfTynGo81PV3aANtT9xE4qVQVqPI+Q81E048qQuGWOVHGIi2peIniWiLiKyOuNEtDoRTSOi56KyGZ679KPOWVU24TA9jrSDx+kkCUtRQ47UTThUA+fTYJnHUp2fAQMay6oWbHV8VX9YVaT1OFxPjduoW6gqT+oiilWZMQvA3gAeiCnzKYDjhRCjAGwN4Cgiskyzkh9V93GEehxphCOvzvG8qKtwhDS05rFT50wXDlfZsggRwrzJI1QVInh1aVyLoC77VkkfhxBiNgBQzFUkhJgHYF70+T0img1gVQDPFWeXfK9DqEqhLpi8Q1V1e3K8bsKRxeP44AP5bhOOqqhSOGx2+MLC0Uxd9q0mZsRDRCMAbAbg8ZgyhxLRDCKasWDBglTbqdrjsI0E+rvfybGj9Hi56XEcc4x818eScqGmBf3sZ2UK61lnZbE4O66n4U0OP1xOKVsWJ5wg31UKdBx6fTnmGDn3d58+wE9/2lhuC3d897vN3ydODLfTF9VgpwlVjRwpBwU02WEHv/+r5AXdDl/SCEfeNyFmJhMA7Lkn8LWv5bsdH/Tr5Gc/K3/7isI8DiKaCsCWhf4DIcTNAesZBOAGAMcKIRa5ygkhJgOYDACjR49OFZWsk8fx9a/L9+98R750TOHYfnv/OOwXv9go+8or6W3NC9+n3v/wh+Jt0RkzJnwo9NGjgfPOk5+XLIkvC7SOdnr66WE2hpBFOF54wb58+nS/myz9WZQy+jjyvH4//dQuRFOm5LeNEPR923vvamwAChQOIUTm+0Mi6g0pGlcKIW7MblU8VXsc+nbjJqivi7uaB0UMI142ppD74upUL4IswpEnod5A1R5H3a61uthTEzNaIdkBcgmA2UKIc8vYZp2e4/ARjiqzPcp8crzupB0dt8wEhbpkVYU2fFV7HHWrl91aOIhoLyKaC2AbALcT0V3R8lWI6I6o2HYAvglgJyKaGb0CZnoIp+pQlb7dugpHUZ3jdbtAQwg5H/p+mvWsO3gcoeeZO8ebqcu+VZVVNQVAS5RQCPEmgPHR54cAlNqctFuoqgjhqGqQw3YWjnbwOOqSVRVKHZ7jqBN1EY6amFEP2i1UtcYaxWy7TDpBOHwuZjXz3ODB7gEZi2wUhgyR7z7DdhSBbRKikP9VFaqqG3WZI70mZtSDdglVEclpL31SRYuC+zga+Ng+caK82z/kEDnP9cMPtzYCRR6DI4+Ud+KHHlrcNuJ47jng2Wdblz/0UHxjqIQjZKiUThaOz3++agskLBwadQpVJd2h7bdfsba44D6OVnxChz17ysYbkHPL254BKLqP46ijilt/EuusI18mSSM6K1EJEY5ODlVV5TGadLA2h1P1WFW+oaoiqWqsqnYWjrxsb+djUBRp+mY62eOoC3yINaoWDt9QVRGENlp5N5bt3GiycBQHC0c94UOs0S6d451EJwhHXllu3OC1wqGqesJVVaPqzvF2Eg7uHG/AHkdxsMdRT/gQa+yzj3zfcMNqtq9X+LTpi2nZdVf5njTrHHeOt5JXQ9WuDd7uuxe37jTpp3VJWS0bNfNkGXTTQ2xnwgRg//2Bvn2r2b7eeJbtbu+2G/DRR+XveycIR3f2OD7+uNi6mkYEQiY06xQ++aTc+sPCYVCVaADVCgdQzb53gnB05z6Ooj3jNMIxaFD+dtSdsr2sNqyqnYvecHSXDr5OEI7u7HEUTZoGsU5zvXcqLBw1omqPIwTuHG/QnT2OokkjHHwci4cPcY2IGzm1LnDneCvscRRHd+3orjs1bZ66J3UViyLpBOFgj6M4WDjqCZ+WGlH38BTAQ47YYI+jOHyF47LLgGWXbXy/6CJglVWKsalqbroJ+Pe/q7WBhaNGtINw5E0nCEdenkI7H4Oi8L0mvvWt5u9VjQJcBnvsUbUFHKqqFd3RLe+ExrIT9qGudMebqXaAhaNGtMNFwp3jrdRhDvhOpZ3rRSfDwlEjuuNF0gnC0c62M0waWDiYSql6ROI8YI+D6W6wcDCpyKuR7AThyGp70sCSDLDxxlVbwOh0w+5YJgt5N/CdIBxZPY677gLmz8/Pnk7j5ZeBIUOqtoLRYeFgKqUThCOr7YMG2efjZiRrrVW1BYxJJaEqItqXiJ4loi4iGp1QticR/YOIbivLPqY8OkE4+IlvprtRVZWfBWBvAA94lP0egNnFmsNURScIRzvbzjBpqEQ4hBCzhRDPJ5UjotUAfAnAxcVbxVRBJwgHZ1Ux3Y26O9m/AfB9AAFT1TPtRPzS72oAAAiTSURBVCcIRzvbzjBpKKxznIimAljZ8tMPhBA3e/x/dwBvCyGeJKIdPcofCuBQAFhjjTUCrWWqohOEgz2OzuOUU4BXX63aivpSmHAIIcZlXMV2AL5CROMB9AOwLBH9RQjxDcf2JgOYDACjR4/mS7hN6AThaGfbGTtnnVW1BfWmtqEqIcQpQojVhBAjAOwP4D6XaDDtCwsHw7QfVaXj7kVEcwFsA+B2IrorWr4KEd1RhU1MGPzkeANOx2W6G5U8ACiEmAJgimX5mwDGW5ZPBzC9cMOYRPjJ8Vba2XaGSQPfKzGV0gnCoeDOcaa7wMLBBKHGDFpppXzWN2iQfB8xIp/1VUEniB7DhMBjVdWMp56q2oJ4JkwAevcG9t8/n/Vtuilw7bXAbrvls74qYY+D6S6wcNSMzTar2oJ4evQAvpFzbtu+++a7vrJhj4PpbnCoimFygj0OprvAwsEwGWGPg+lusHAwDMMwQbBwMAzDMEGwcDBMTnAfB9NdYOFgmIxwHwfT3WDhYJicYI+D6S6wcDBMRtjjYLobLBwMkxPscTDdBRYOhskIexxMd4OFg2Eyoubj6N+/WjsYpixYOBgmIyNGAGeeCdx6a9WWMEw58CCHDJMRIuCHP6zaCoYpD/Y4GIZhmCBYOBiGYZggWDgYhmGYIFg4GIZhmCBYOBiGYZggWDgYhmGYIFg4GIZhmCBYOBiGYZggSHTgyGxEtADAayn/PgTAv3M0px3gfe4e8D53Pln29zNCiKE+BTtSOLJARDOEEKOrtqNMeJ+7B7zPnU9Z+8uhKoZhGCYIFg6GYRgmCBaOViZXbUAF8D53D3ifO59S9pf7OBiGYZgg2ONgGIZhgmDhiCCiXYnoeSJ6iYhOrtqevCCi1YloGhE9R0TPEtH3ouWDiegeInoxel8hWk5E9NvoODxNRJ+rdg/SQ0Q9iegfRHRb9H1NIno82rdriKhPtLxv9P2l6PcRVdqdFiJanoiuJ6I5RDSbiLbp9PNMRMdF9XoWEV1FRP067TwT0aVE9DYRzdKWBZ9XIpoQlX+RiCZksYmFA7KBAfB7ALsBGAXgACIaVa1VufEpgOOFEKMAbA3gqGjfTgZwrxBiJIB7o++APAYjo9ehAP5Qvsm58T0As7XvvwDwayHEOgAWAjg4Wn4wgIXR8l9H5dqR8wD8TQixPoBNIPe9Y88zEa0K4BgAo4UQGwHoCWB/dN55vhzArsayoPNKRIMB/AjAVgC2BPAjJTapEEJ0+xeAbQDcpX0/BcApVdtV0L7eDGBnAM8DGB4tGw7g+ejzRQAO0Mr/f7l2egFYLbqgdgJwGwCCfDCql3nOAdwFYJvoc6+oHFW9D4H7uxyAV0y7O/k8A1gVwP8CGBydt9sAfLETzzOAEQBmpT2vAA4AcJG2vKlc6Is9DomqgIq50bKOInLNNwPwOIBhQoh50U/zAQyLPnfKsfgNgO8D6Iq+rwjgv0KIT6Pv+n79/z5Hv78blW8n1gSwAMBlUXjuYiIaiA4+z0KINwCcA+B1APMgz9uT6OzzrAg9r7mebxaObgIRDQJwA4BjhRCL9N+EvAXpmPQ6ItodwNtCiCertqVEegH4HIA/CCE2A/A+GuELAB15nlcAsAekaK4CYCBaQzodTxXnlYVD8gaA1bXvq0XLOgIi6g0pGlcKIW6MFr9FRMOj34cDeDta3gnHYjsAXyGiVwFcDRmuOg/A8kTUKyqj79f/73P0+3IA3inT4ByYC2CuEOLx6Pv1kELSyed5HIBXhBALhBCfALgR8tx38nlWhJ7XXM83C4fkCQAjo2yMPpAdbLdUbFMuEBEBuATAbCHEudpPtwBQmRUTIPs+1PKDouyMrQG8q7nEbYEQ4hQhxGpCiBGQ5/I+IcTXAUwD8NWomLnP6lh8NSrfVnfmQoj5AP6XiNaLFn0BwHPo4PMMGaLamogGRPVc7XPHnmeN0PN6F4BdiGiFyFPbJVqWjqo7feryAjAewAsAXgbwg6rtyXG/tod0Y58GMDN6jYeM7d4L4EUAUwEMjsoTZIbZywCegcxYqXw/Muz/jgBuiz6vBeDvAF4CcB2AvtHyftH3l6Lf16ra7pT7uimAGdG5vgnACp1+ngGcAWAOgFkA/gygb6edZwBXQfbhfALpWR6c5rwC+E607y8B+HYWm/jJcYZhGCYIDlUxDMMwQbBwMAzDMEGwcDAMwzBBsHAwDMMwQbBwMAzDMEGwcDBMDES0OHofQUQH5rzuU43vj+S5foYpChYOhvFjBIAg4dCeXnbRJBxCiG0DbWKYSmDhYBg/JgEYQ0QzozkgehLRL4noiWjeg8MAgIh2JKIHiegWyKeYQUQ3EdGT0bwRh0bLJgHoH63vymiZ8m4oWvcsInqGiL6mrXs6NebcuDJ6YpphSiXpjohhGMnJAE4QQuwOAJEAvCuE2IKI+gJ4mIjujsp+DsBGQohXou/fEUL8h4j6A3iCiG4QQpxMREcLITa1bGtvyKfANwEwJPrPA9FvmwHYEMCbAB6GHJvpofx3l2HcsMfBMOnYBXJMoJmQw9SvCDl5DgD8XRMNADiGiP4J4DHIgeZGIp7tAVwlhFgqhHgLwP0AttDWPVcI0QU5fMyIXPaGYQJgj4Nh0kEAviuEaBoojoh2hBzSXP8+DnICoQ+IaDrkmElpWaJ9Xgq+hpkKYI+DYfx4D8Ay2ve7ABwRDVkPIlo3mjjJZDnI6Uo/IKL1IafvVXyi/m/wIICvRf0oQwF8HnJQPoapBXy3wjB+PA1gaRRyuhxyfo8RAJ6KOqgXANjT8r+/ATiciGZDTuP5mPbbZABPE9FTQg77rpgCOeXpPyFHNv6+EGJ+JDwMUzk8Oi7DMAwTBIeqGIZhmCBYOBiGYZggWDgYhmGYIFg4GIZhmCBYOBiGYZggWDgYhmGYIFg4GIZhmCBYOBiGYZgg/g+zinzY6ILxeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "L=10\n",
    "Nwarmup = 100\n",
    "Nsteps = 1000\n",
    "Ndecorr = 3\n",
    "Temp = 3\n",
    "J = 1.\n",
    "\n",
    "S = Ising(L, J, Temp)\n",
    "E = np.zeros(Nsteps)\n",
    "M = np.zeros(Nsteps)\n",
    "\n",
    "for i in range(Nwarmup):\n",
    "    S.metropolis()\n",
    "\n",
    "naccept = 0\n",
    "for i in range(Nsteps):\n",
    "    for n in range(Ndecorr):\n",
    "        naccept += S.metropolis()\n",
    "    E[i] = S.E\n",
    "    M[i] = abs(S.Mtot)\n",
    "\n",
    "E /= S.N\n",
    "M /= S.N\n",
    "\n",
    "\n",
    "Et = np.sum(E)/Nsteps\n",
    "E2t = np.sum(E**2)/Nsteps\n",
    "Mt = np.sum(M)/Nsteps\n",
    "M2t = np.sum(M**2)/Nsteps\n",
    "\n",
    "print(\"T = \", Temp)\n",
    "print(\"<E>/N = \", Et)\n",
    "print(\"<E^2>/N = \", E2t)\n",
    "print(\"<M>/N = \", Mt)\n",
    "print(\"<M^2>/N = \", M2t)\n",
    "print(\"C=\", (E2t-Et*Et)/Temp/Temp)\n",
    "print(\"chi=\", (M2t-Mt*Mt)/Temp)\n",
    "print(\"Acceptance ratio = \", float(naccept)/S.N/Nsteps/Ndecorr)\n",
    "        \n",
    "pyplot.plot(np.arange(0,Nsteps,1),E,ls='-',c='blue');\n",
    "pyplot.xlabel(\"Iteration\")\n",
    "pyplot.ylabel(\"Energy\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(np.arange(0,Nsteps,1),M,ls='-',c='red');\n",
    "pyplot.xlabel(\"Iteration\")\n",
    "pyplot.ylabel(\"Magnetization\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2 100000.0 1.0\n",
      "0.4 100000.0 1.0\n",
      "0.6000000000000001 100000.0 1.0\n",
      "0.8 99992.0 0.99992\n",
      "1.0 99942.0 0.99942\n",
      "1.2 99702.0 0.99702\n",
      "1.4000000000000001 99128.0 0.99128\n",
      "1.6 98086.0 0.98086\n",
      "1.8 95720.0 0.9571999999999999\n",
      "2.0 90848.0 0.90848\n",
      "2.2 80178.0 0.8017799999999999\n",
      "2.4000000000000004 66042.0 0.66042\n",
      "2.6000000000000005 45392.0 0.45392000000000005\n",
      "2.8000000000000003 36088.0 0.36088000000000003\n",
      "3.0000000000000004 27252.0 0.27252\n",
      "3.2 23986.0 0.23986000000000002\n",
      "3.4000000000000004 21472.0 0.21472000000000002\n",
      "3.6000000000000005 18714.0 0.18713999999999997\n",
      "3.8000000000000003 18534.0 0.18533999999999998\n",
      "4.0 16042.0 0.16042\n",
      "4.2 16450.0 0.16449999999999998\n",
      "4.4 15248.0 0.15248\n",
      "4.6000000000000005 14750.0 0.1475\n",
      "4.800000000000001 14170.0 0.1417\n",
      "5.000000000000001 13548.0 0.13548\n",
      "5.2 12864.0 0.12864\n",
      "5.4 12714.0 0.12714\n",
      "5.6000000000000005 12526.0 0.12526\n",
      "5.800000000000001 12084.0 0.12084\n",
      "6.000000000000001 12092.0 0.12092\n",
      "6.2 12198.0 0.12198\n",
      "6.4 11662.0 0.11662\n",
      "6.6000000000000005 11182.0 0.11182\n",
      "6.800000000000001 11772.0 0.11772\n",
      "7.000000000000001 11436.0 0.11436\n",
      "7.2 11260.0 0.11259999999999999\n",
      "7.4 10568.0 0.10568\n",
      "7.6000000000000005 10802.0 0.10801999999999999\n",
      "7.800000000000001 10558.0 0.10558\n"
     ]
    }
   ],
   "source": [
    "T = np.arange(0.2,8,0.2)\n",
    "\n",
    "Mt = np.zeros(T.size)\n",
    "Et = np.zeros(T.size)\n",
    "M2t = np.zeros(T.size)\n",
    "E2t = np.zeros(T.size)\n",
    "\n",
    "S = Ising(L, J, 0.2)\n",
    "\n",
    "Nsteps = 1000\n",
    "Nwarmup = 10000\n",
    "n = 0\n",
    "for t in T:\n",
    "    S.set_temp(t)\n",
    "    for i in range(Nwarmup):\n",
    "        S.metropolis()\n",
    "\n",
    "    for i in range(Nsteps):\n",
    "        for j in range(Ndecorr):\n",
    "            S.metropolis()\n",
    "        Et[n] += S.E\n",
    "        Mt[n] += abs(S.Mtot)\n",
    "        E2t[n] += S.E**2\n",
    "        M2t[n] += abs(S.Mtot)**2\n",
    "\n",
    "    print(t, Mt[n], Mt[n]/Nsteps/S.N)\n",
    "    n += 1\n",
    "\n",
    "Mt /= float(Nsteps*S.N)\n",
    "Et /= float(Nsteps*S.N)\n",
    "E2t /= float(Nsteps*S.N*S.N)\n",
    "M2t /= float(Nsteps*S.N*S.N)\n",
    "ErrorE = np.sqrt((E2t-Et**2)/Nsteps)\n",
    "ErrorM = np.sqrt((M2t-Mt**2)/Nsteps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(T,Mt,ls='-',c='blue')\n",
    "pyplot.errorbar(T, Mt, yerr=[ErrorM, ErrorM], fmt='--o')\n",
    "pyplot.ylabel(\"Magnetization\")\n",
    "pyplot.xlabel(\"Temperature\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(T,Et,ls='-',c='blue')\n",
    "pyplot.errorbar(T, Et, yerr=[ErrorE, ErrorE], fmt='--o')\n",
    "pyplot.ylabel(\"Energy\")\n",
    "pyplot.xlabel(\"Temperature\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(T,(E2t-Et**2)/T/T,marker='o',ls='-',c='blue');\n",
    "pyplot.ylabel(\"Cv\")\n",
    "pyplot.xlabel(\"Temperature\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(T,(M2t-Mt**2)/T,marker='o',ls='-',c='blue');\n",
    "pyplot.ylabel(\"Chi\")\n",
    "pyplot.xlabel(\"Temperature\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = np.meshgrid(np.arange(0,L,1),np.arange(0,L,1))\n",
    "s = S.spin.reshape(L,L)\n",
    "pyplot.pcolormesh(x,y,s)\n",
    "pyplot.ylabel(\"Y\")\n",
    "pyplot.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
       "css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<div class=\"animation\" align=\"center\">\n",
       "    <img id=\"_anim_img15fb06eb828144f2afe4cdfcc854f1fa\">\n",
       "    <br>\n",
       "    <input id=\"_anim_slider15fb06eb828144f2afe4cdfcc854f1fa\" type=\"range\" style=\"width:350px\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           onchange=\"anim15fb06eb828144f2afe4cdfcc854f1fa.set_frame(parseInt(this.value));\"></input>\n",
       "    <br>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.previous_frame()\">\n",
       "        <i class=\"fa fa-step-backward\"></i></button>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.reverse_animation()\">\n",
       "        <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.pause_animation()\"><i class=\"fa fa-pause\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.play_animation()\"><i class=\"fa fa-play\"></i>\n",
       "        </button>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.next_frame()\"><i class=\"fa fa-step-forward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim15fb06eb828144f2afe4cdfcc854f1fa.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
       "  <form action=\"#n\" name=\"_anim_loop_select15fb06eb828144f2afe4cdfcc854f1fa\" class=\"anim_control\">\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"once\" > Once </input>\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"loop\" checked> Loop </input>\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"reflect\" > Reflect </input>\n",
       "  </form>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img15fb06eb828144f2afe4cdfcc854f1fa\";\n",
       "    var slider_id = \"_anim_slider15fb06eb828144f2afe4cdfcc854f1fa\";\n",
       "    var loop_select_id = \"_anim_loop_select15fb06eb828144f2afe4cdfcc854f1fa\";\n",
       "    var frames = new Array(30);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
       "AAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBo\\\n",
       "dHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAFk9JREFUeJzt3W9oVHe+x/FPumlcrmh2yyZNzBit\\\n",
       "rZhJ0sXEWcLCsmglbSmioGGpWG5blXB7l3vbK33gpY/2yRoK3dZ2+yRQulKhYXG5a6mtoOlKwdZd\\\n",
       "hnj3IhIRSaoTo1hM/ZeaNHHuA5lk5mTMnJlM8jvfM+8XLJuZTOw3w+R85vObM78pSyaTSQEAYMxD\\\n",
       "rgcAAKAQBBgAwCQCDABgEgEGADCJAAMAmESAAQBMIsAAACYRYAAAkwgwAIBJBBgAwCQCDABgEgEG\\\n",
       "ADCJAAMAmESAAQBMIsAAACYRYAAAkwgwAIBJBBgAwCQCDABgEgEGADCJAAMAmESAAQBMIsAAACYR\\\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim15fb06eb828144f2afe4cdfcc854f1fa = new Animation(frames, img_id, slider_id, 100.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "# Animation\n",
    "\n",
    "S.set_temp(2.27) #2.27\n",
    "S.spin.fill(1)\n",
    "\n",
    "fig, ax = pyplot.subplots()\n",
    "ax = pyplot.axes(xlim=(0, L), ylim=(0, L))\n",
    "Sdata = S.spin.reshape(L,L)\n",
    "cont = ax.contourf(x,y,Sdata)\n",
    "\n",
    "def evolve(i):\n",
    "    global x, y, S\n",
    "    S.metropolis()\n",
    "    Sdata = S.spin.reshape(L,L)\n",
    "    cont = ax.contourf(x,y,Sdata)\n",
    "    return cont,\n",
    "\n",
    "anim = animation.FuncAnimation(fig, evolve, frames = 30, interval=100, blit = False)\n",
    "\n",
    "HTML(anim.to_jshtml())            \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Challenge 11.2\n",
    "\n",
    "Modify the code to calculate the correlation function \n",
    "\n",
    "$$ C(r) = \\langle s_0 s_r \\rangle - \\langle s_0 \\rangle \\langle s_r \\rangle $$\n",
    "\n",
    "Plot the correlations along the $x$ direction across the phase transition and describe its behavior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}