Notebooks/IsingModel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PYTHON VERSION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6.5 |Anaconda, Inc.| (default, Mar 29 2018, 13:32:41) [MSC v.1900 64 bit (AMD64)]\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "print(sys.version)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 6)  # increase default figure size\n",
    "\n",
    "np.random.seed(2016)  # for reproducibility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ising Model\n",
    "\n",
    "\n",
    "In this notebook the **Metropolis-Hastings** algorithm will be used to\n",
    "sample from the invariant distribution $\\pi$ of the [Ising model](https://en.wikipedia.org/wiki/Ising_model). \n",
    "In the next code cell a grid of length `L = 32` is considered, \n",
    "therefore the space $\\mathbb{X}$ of possible configurations has a cardinality of $2^{1024} > 10^{307}$. \n",
    "Clearly, sampling from such a large space is practically impossible with conventional methods. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters\n",
    "L = 32  # length of lattice\n",
    "N = L * L  # number of particles\n",
    "nsteps = N * 800  # number of updates, we will update each spin 800 times on average \n",
    "Temperature = 30.  # in units where the Boltzmann factor is 1\n",
    "\n",
    "# Initialize Variables\n",
    "spins = 2 * (np.random.rand(L, L) > 0.5) - 1  # random initial state (table of {1, -1})\n",
    "kernel = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]])\n",
    "\n",
    "for n in range(nsteps):\n",
    "    r, c = np.random.randint(0, L, 2)  # select a vertex (row, column) at random\n",
    "    # indices of a box around r, c\n",
    "    C = [(c-1) % L, c % L, (c + 1) % L]  # periodic boundary conditions, i.e. (0,x) is a neighbour of (L-1,x) \n",
    "    R = [[(r-1) % L], [r % L], [(r+1) % L]]\n",
    "    DH = spins[r, c] * np.sum(kernel * spins[R, C]) \n",
    "    if np.random.rand() < np.exp(- DH / Temperature):  \n",
    "        spins[r, c] *= -1  # flip spin \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code uses the Metropolis-Hastings algorithm \n",
    "to simulate a Markovian chain on $\\mathbb{X}$ \n",
    "starting from a random initial configuration (`spins`) and having an invariant distribution of the [Gibbs measure](https://en.wikipedia.org/wiki/Gibbs_measure) corresponding to the energy of the Ising model, i.e.\n",
    "\n",
    "$$H(\\sigma)=-\\sum_{x,y: x~y} \\sigma(x)\\sigma(y)$$\n",
    "and\n",
    "$$\\pi(\\sigma)=\\frac{e^{-\\beta H(\\sigma)}}{Z(\\beta)}$$\n",
    "where the partition function $Z(\\beta)$ is given by\n",
    "$$Z(\\beta)=\\sum_{\\sigma\\in\\mathbb{X}} e^{-\\beta H(\\sigma)}.$$\n",
    "\n",
    "\n",
    "In each iteration (`nsteps`)\n",
    "randomly selects a point on the grid (`r, c`) and calculates the difference in energy \n",
    "of the system (`DH`) if the spin at that point changes sign. \n",
    "It then accepts or rejects the spin change with probability $e^{-\\beta (DH)^+}$, as defined by the Metropolis-Hastings algorithm.\n",
    "\n",
    "In the next code cell the final state of the system is visualized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(spins, cmap='binary', vmin=-1, vmax=1, interpolation='nearest')\n",
    "plt.title(\"Temperature: %.1f, Grid Size: %d\" % (Temperature, L))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ising Parameters\n",
    "\n",
    "To get a better intuition of how the system works, its behavior will be studied by tweaking the various parameters.\n",
    "\n",
    "First the question of how energy affects the probability of spin change will be studied.\n",
    "In the code cell below the transition probability for all the\n",
    "possible energy values is plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-4, 5)  # all possible DH after a spin flip\n",
    "Temperature = 3.0\n",
    "y = np.exp(-np.maximum(x,0) / Temperature)  \n",
    "plt.plot(x, y)\n",
    "plt.xlabel(\"Energy Difference\")\n",
    "plt.ylabel(\"Transition Probability\")\n",
    "plt.grid(True)\n",
    "plt.axvline(0, color='red', linestyle='dashed')\n",
    "plt.axhline(1, color='red', linestyle='dashed')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that when the energy of the system decreases (`DH < 0`),\n",
    "the algorithm automatically accepts the proposed change. On the contrary, when the system energy increases,\n",
    "the algorithm does not immediately reject the change but accepts it with decreasing probability.\n",
    "\n",
    "In the next code various temperatures are tested to see how they affect\n",
    "the probability of a spin change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "temperatures = [1, 2, 5, 10, 20, 50]\n",
    "cmap = plt.cm.get_cmap('Dark2')\n",
    "colors = [cmap(x) for x in np.linspace(0, 1, 6)]\n",
    "\n",
    "for col, temp in zip(colors, temperatures):\n",
    "    y = np.exp(-np.maximum(x,0) / temp)\n",
    "    plt.semilogy(x, y, label='T=%d' % temp)\n",
    "\n",
    "plt.xlabel(\"Energy Difference\")\n",
    "plt.ylabel(\"Transition Probability\")\n",
    "plt.grid(True)\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how temperature (`T`) \"controls\" the slope of the logarithm of the transition probability.\n",
    "A small temperature (and therefore a large slope) means that the chain is very sensitive\n",
    "to changes in energy, so the only changes it will accept are those that\n",
    "decrease the energy of the system or increase it only slightly. In contrast, a high temperature\n",
    "(and therefore a small gradient) means that the chain is essentially indifferent to\n",
    "the energy of the system and accepts any proposed change since, as we can see\n",
    "the probability of a spin change is close to one.\n",
    "\n",
    "### Ising Animation\n",
    "\n",
    "For the next code cell the script `animate_ising.py` is required. This script visualizes dynamically the evolution of the spin grid.\n",
    "\n",
    "It takes 3 arguments\n",
    "\n",
    "1. `-L`: the size of the lattice\n",
    "2. `-Temp`: the temperature\n",
    "3. `-up`: the percentage of spins that are initially positive\n",
    "\n",
    "Try running the following cell after deleting `#` from the first 2 lines\n",
    "depending on your operating system. If it does not run, open a command window (Terminal) and from the folder where you have saved the `animate_ising.py` file and type the command `python3 animate_ising.py -T 0.1 -L 32 -up 0.5`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vXnL3LkYToUKiCVHH1JFcRJyKiNeL2x8wmixmM4mPSUkdScVI65PmdhH+zcCvV3zf5eSfAfxQ0pKkhY5quODaiDgFoxchcE2Htdwn6Ujxa0Hrv36sJGkro/kjDtHhMbmkDkh8TFJMmttF+Feb0qSrlsNtEXEL8MfAtyR9oaM6+uQJ4EZGazScAh5JtWNJVwIvAPdHxPup9luhjuTHJKaYNLeqLsJ/Atiy4vuxk3+2LSJOFl/PAC/R7cxEpyVtAii+numiiIg4XbzwzgNPkuiYSFrPKHBPR8SLxd3Jj8lqdXR1TIp9r3nS3Kq6CP9rwLbiyuUVwN3A/tRFSPq4pKsu3Aa+DBwtf1ar9jOaCBU6nBD1QtgKd5HgmGg0wd1TwLGIeHTFj5Iek3F1pD4mySbNTXUF85KrmXcwupL6S+DPO6rhU4w6DW8Ab6WsA3iG0dvH/2X0Tuhe4PeAA8Aviq8bOqrj74E3gSOMwrcpQR2fZ/QW9ghwuPhzR+pjUlJH0mMCfJbRpLhHGP1H8xcrXrM/Ad4G/hH46DT78Sf8zDLlT/iZZcrhN8uUw2+WKYffLFMOv1mmHH6zTDn8Zply+M0y9X+rH6/xEV4DWQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run animate_ising.py -T 0.1 -L 32 -up 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But let the program run long enough to see the system end up to a state where th spins are either (almost) all +1, or (almost) all -1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following code cell the `Ising` function is given and it can be executed provided \n",
    "\n",
    "1. The initial state of the grid (a numpy array with -1 and 1).\n",
    "2. The temperature.\n",
    "3. Optionally, the number of steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Ising(spins_init, Temp, nsteps=None):\n",
    "    \"\"\"\n",
    "    Ising Model.\n",
    "        spins_init: initial configuration\n",
    "        Temp: the Temperature\n",
    "        updates: the number of updates to perform\n",
    "    \"\"\"\n",
    "    spins = spins_init.astype(np.int8)  # copy and save some space :)\n",
    "    L = spins.shape[0]\n",
    "    N = L * L\n",
    "    kernel = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]], dtype=np.int8)\n",
    "    Temp = Temp\n",
    "    if nsteps is None:\n",
    "        nsteps = L * L * 800  # number of updates\n",
    "\n",
    "    for n in range(nsteps):\n",
    "        r, c = np.random.randint(0, L, 2)  # select a vertex at random\n",
    "        C = [(c-1) % L, c % L, (c + 1) % L]\n",
    "        R = [[(r-1) % L], [r % L], [(r+1) % L]]\n",
    "        DH = -spins[r, c] * np.sum(kernel * spins[R, C]) / Temp\n",
    "        if np.log(np.random.rand()) < DH:\n",
    "            spins[r, c] *= -1  # switch sign\n",
    "    \n",
    "    return spins"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Application\n",
    "\n",
    "(a) Try running the code with all spins initially at +1. \n",
    "\n",
    "(b) Now start lowering the temperature, successively setting \n",
    "T = 30, 10, 5, 2, 1.5, 1., 0.5, 0.1, 0.01. Show for each temperature the picture you got.\n",
    "\n",
    "The magnetization of the system is defined as the average spins of the lattice $\\Lambda$, i.e.\n",
    "\n",
    "$$ m(\\sigma) = \\frac{1}{|\\Lambda|} \\sum_{k \\in \\Lambda} \\sigma(k) $$\n",
    "\n",
    "(c) Consider how $m(\\sigma)$ behaves for the states $\\sigma$ \n",
    "given by the algorithm as you lower the temperature, as in question (b).\n",
    "Show a plot of $m(\\sigma)$ versus temperature (for the $\\sigma$ configuration you simulated).\n",
    "\n",
    "(d) For the temperature `T = 0.1` change the value of the parameter nsteps. What do the intermediate stages through which the chain passes look like until it reaches the point where it resembles the picture obtained for `nsteps = 800 × L × L`? Show the images you obtained for `nsteps=10,20,50,100,100,200,400,800 × L × L`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy.matlib\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 6)  # increase default figure size\n",
    "\n",
    "np.random.seed(2016)  # for reproducibility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Application \n",
    "# Question (a)\n",
    "# Parameters\n",
    "L = 32             # length of lattice\n",
    "N = L * L          # number of particles\n",
    "nsteps = N * 800   # number of updates, we will update each spin 800 times on average \n",
    "Temperature = 30.  # in units where the Boltzmann factor is 1\n",
    "\n",
    "# Initialize Variables\n",
    "spins = np.matlib.ones((L,L))  # initial state (LxLtable of ones)\n",
    "kernel = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]])\n",
    "\n",
    "for n in range(nsteps):\n",
    "    r, c = np.random.randint(0, L, 2)                  # select a vertex (row, column) at random\n",
    "    # indices of a box around r, c\n",
    "    C = [(c-1) % L, c % L, (c + 1) % L]                # periodic boundary conditions, i.e. (0,x) is a neighbour of (L-1,x) \n",
    "    R = [[(r-1) % L], [r % L], [(r+1) % L]]\n",
    "    DH = spins[r, c] * np.sum(kernel * spins[R, C])    \n",
    "    if np.random.rand() < np.exp(- DH / Temperature):  \n",
    "        spins[r, c] *= -1  # flip spin "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting\n",
    "plt.imshow(spins, cmap='binary', vmin=-1, vmax=1, interpolation='nearest')\n",
    "plt.title(\"Temperature: %.1f, Grid Size: %d\" % (Temperature, L))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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btjA/P7+eq7zfUAOFrsRQ5cpDDm476yX2MH4bN1Jfhny/TPr1PY3y/kk+P3Nz4/0gqXvWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUgHWtYJy0IasIxzXr1VOtGLIvG+k10cIgsy20cYjXo3vWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUgJmsYJxGhd5QVWjTGHuuhcrEFsYjHMqQY1mOa8iqzVkfi3Qa6x6He9aS1ADDWpIaYFhLUgMMa0lqgGEtSQ0wrCWpAYa1JDXAsJakBhjWktSAda1g3LZt20Qro4asBNuMlXfTMFQ15pDbbxqvsaH6M41qw0k/PxtlHFT3rCWpAcuGdZIzk9yc5MqRaacm+XaSy/vLc6fbTEna3MbZs34PcNwi099eVUf1lwsn2yxJ0qhlw7qqLgFuW4e2SJKWsJZj1qck+Xx/mGSfibVIkvRjVhvW7wAeAxwF3Ai8bakZk2xNMp9kfpXrkqRNb1VhXVU3VdW9VXUf8C7gmB3Me0ZVzVXV3GobKUmb3arCOsmBIzefB1y51LySpLVbtigmyfuBpwP7JbkeeAPw9CRHAQVcA7xyim2UpE0v61lBlmSslQ1ZcTQuKx13bNbHiWxhHMRpGLLqb1wtvFenUGW57IxWMEpSAwxrSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIaYFhLUgMMa0lqwLoOmLtlyxbm55f/pdQhS2KHLLOd9RL2FkqQh3xNtFDKPdRrbMgBc1vYLuNwz1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUAMNakhqwrhWM27ZtG6uaqJEBLsde92Y01PM4jerOoSpGN+ugvhvJOM/33NzcWMtyz1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUAMNakhowk2MwTsNQFXUrWd6k2zhU5R20MdbfuIZ8HiethcpSqywX5561JDXAsJakBhjWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1oOkxGFdiI1XUDWUaVWgb6fnZSH0ZklWWi3PPWpIasGxYJzkkySeSXJ3kqiSv7qfvm+SiJF/t/+4z/eZK0uY0zp71PcDvVNXjgGOBVyU5Avh94OKqOhy4uL8tSZqCZcO6qm6sqsv663cBVwMHAccDZ/WznQWcMK1GStJmt6Jj1kkOA44GLgUeXlU3QhfowAGTbpwkqTP22SBJ9gTOA15TVXeO+81pkq3A1tU1T5IEY+5ZJ9mVLqjPrqrz+8k3JTmwv/9A4ObFHltVZ1TVXFXNTaLBkrQZjXM2SIB3A1dX1ekjd10AnNRfPwn46OSbJ0mC8Q6DPAV4KfCFJJf3014HnAZ8IMkrgG8BL5xOEyVJy4Z1VX0aWOoA9c9PtjmSpMXM5IC5G2mg12n0ZaiBdS2nXl9DDv476dfENAaOnvTyZv31bbm5JDXAsJakBhjWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1IOtZtZNksBKhIQfXnLRZr7SC4QYenka12kapgFuJIV/fkzZkJei4qmrZBbpnLUkNMKwlqQGGtSQ1wLCWpAYY1pLUAMNakhpgWEtSAwxrSWqAYS1JDVjXMRjHNelqtZWwWm1pK+lzC2NZDqWF11gL43dutteOe9aS1ADDWpIaYFhLUgMMa0lqgGEtSQ0wrCWpAYa1JDXAsJakBhjWktSAmaxgbEELVWjjamSMukHWu5J1T3p5K+nLrL/Ohtwusz4u59zc3FjLcs9akhpgWEtSAwxrSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIasGkqGFuoONxIVX+TNuk2tlDpOA0tvA8mbaP0xT1rSWrAsmGd5JAkn0hydZKrkry6n35qkm8nuby/PHf6zZWkzWmcwyD3AL9TVZcl2QvYluSi/r63V9Vbp9c8SRKMEdZVdSNwY3/9riRXAwdNu2GSpB9Z0THrJIcBRwOX9pNOSfL5JGcm2WfCbZMk9cYO6yR7AucBr6mqO4F3AI8BjqLb837bEo/bmmQ+yfwE2itJm9JYYZ1kV7qgPruqzgeoqpuq6t6qug94F3DMYo+tqjOqaq6qxvuFbUnSjxnnbJAA7waurqrTR6YfODLb84ArJ988SRKMdzbIU4CXAl9Icnk/7XXAiUmOAgq4BnjlVFooSRrrbJBPA4uVPV04+eZIkhbTdLl5CwO9TsNQA7iuxEYqnW+hXHnSZeSbsSx91t/7lptLUgMMa0lqgGEtSQ0wrCWpAYa1JDXAsJakBhjWktQAw1qSGmBYS1IDmq5gnIaNNMjskCZd2bYZn++VPIdDVYxOg31ZnHvWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUACsYV6mFcQuHrATbjBWH4xryuRlqbMWV9LmF6tchKp3ds5akBhjWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAasawXjli1bmJ+fX3a+FiqONtJYjdPoy5Dj3k3aUFV/0zBUdeA0ql8n3ZdZ337uWUtSAwxrSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIaYFhLUgMMa0lqwEwOmLuRSrmnYSP1e6i+rKS0eCOVNU+6lHsjvVdnvY3L7lkn2T3JZ5NckeSqJG/spz86yaVJvprk3CS7Tb+5krQ5jXMY5IfAM6rqicBRwHFJjgX+CHh7VR0O3A68YnrNlKTNbdmwrs7d/c1d+0sBzwA+1E8/CzhhKi2UJI33BWOSnZNcDtwMXAR8Hbijqu7pZ7keOGg6TZQkjRXWVXVvVR0FHAwcAzxusdkWe2ySrUnmk8zfcsstq2+pJG1iKzp1r6ruAD4JHAvsnWT72SQHAzcs8Zgzqmququb233//tbRVkjatcc4G2T/J3v31BwHPBK4GPgG8oJ/tJOCj02qkJG1245xnfSBwVpKd6cL9A1X1V0m+CJyT5E3APwDvnmI7JWlTWzasq+rzwNGLTP8G3fFrSdKUzWQF47imUQk21MC60zDrFVnQRgXcRnoexzXpPk9jwNwWjNPvubm5sZblb4NIUgMMa0lqgGEtSQ0wrCWpAYa1JDXAsJakBhjWktQAw1qSGmBYS1IDsp4VdkluAa5dMHk/4NZ1a8R02ZfZZF9mk33pPKqqlv1J0nUN60UbkMxX1Xj1ljPOvswm+zKb7MvKeBhEkhpgWEtSA2YhrM8YugETZF9mk32ZTfZlBQY/Zi1JWt4s7FlLkpYxaFgnOS7Jl5N8LcnvD9mWtUpyTZIvJLk8yfzQ7VmJJGcmuTnJlSPT9k1yUZKv9n/3GbKN41qiL6cm+Xa/bS5P8twh2ziOJIck+USSq5NcleTV/fTmtssO+tLidtk9yWeTXNH35Y399EcnubTfLucm2W3i6x7qMEg/puNXgGcB1wOfA06sqi8O0qA1SnINMFdVzZ03muRpwN3Ae6vq8f20twC3VdVp/T/Sfarq94Zs5ziW6MupwN1V9dYh27YSSQ4EDqyqy5LsBWwDTgBeRmPbZQd9+VXa2y4B9qiqu5PsCnwaeDXw28D5VXVOkncCV1TVOya57iH3rI8BvlZV36iqfwbOAY4fsD2bVlVdAty2YPLxwFn99bPo3lwzb4m+NKeqbqyqy/rrdwFXAwfR4HbZQV+aU527+5u79pcCngF8qJ8+le0yZFgfBFw3cvt6Gt2AvQI+lmRbkq1DN2YCHl5VN0L3ZgMOGLg9a3VKks/3h0lm/tDBqCSH0Q1afSmNb5cFfYEGt0uSnZNcDtwMXAR8Hbijqu7pZ5lKlg0Z1ouNitnyqSlPqaonAc8BXtV/HNdseAfwGOAo4EbgbcM2Z3xJ9gTOA15TVXcO3Z61WKQvTW6Xqrq3qo4CDqY7QvC4xWab9HqHDOvrgUNGbh8M3DBQW9asqm7o/94MfJhuI7bspv5Y4/ZjjjcP3J5Vq6qb+jfYfcC7aGTb9MdEzwPOrqrz+8lNbpfF+tLqdtmuqu4APgkcC+ydZJf+rqlk2ZBh/Tng8P5b1N2AFwMXDNieVUuyR//FCUn2AJ4NXLnjR828C4CT+usnAR8dsC1rsj3ces+jgW3Tf5H1buDqqjp95K7mtstSfWl0u+yfZO/++oOAZ9Idg/8E8IJ+tqlsl0GLYvpTdf4E2Bk4s6rePFhj1iDJT9DtTQPsAryvpb4keT/wdLpfDrsJeAPwEeADwKHAt4AXVtXMf3G3RF+eTvdRu4BrgFduP+47q5I8Ffg/wBeA+/rJr6M71tvUdtlBX06kve3yBLovEHem29n9QFX9YZ8B5wD7Av8AvKSqfjjRdVvBKEmzzwpGSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIaYFhLUgP+Px6TIYZL77jRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question (b)\n",
    "# Parameters\n",
    "L = 32               \n",
    "N           = L * L            \n",
    "nsteps      = N * 100 # I changed the update-rate\n",
    "T           = [30, 10, 5, 2, 1.5, 1, 1.0, 0.5, 0.1, 0.01]\n",
    "\n",
    "for Temperature in T:\n",
    "    # Initialize Variables\n",
    "    spins = 2 * (np.random.rand(L, L) > 0.5) - 1  \n",
    "    kernel = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]])\n",
    "\n",
    "    for n in range(nsteps):\n",
    "        r, c = np.random.randint(0, L, 2)                  # select a vertex (row, column) at random\n",
    "        # indices of a box around r, c\n",
    "        C = [(c-1) % L, c % L, (c + 1) % L]                # periodic boundary conditions, i.e. (0,x) is a neighbour of (L-1,x) \n",
    "        R = [[(r-1) % L], [r % L], [(r+1) % L]]\n",
    "        DH = spins[r, c] * np.sum(kernel * spins[R, C])   \n",
    "        if np.random.rand() < np.exp(- DH / Temperature):  \n",
    "            spins[r, c] *= -1  # flip spin \n",
    "\n",
    "    # Plotting\n",
    "    plt.imshow(spins, cmap='binary', vmin=-1, vmax=1, interpolation='nearest')\n",
    "    plt.title(\"Temperature: %.1f, Grid Size: %d\" % (Temperature, L))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For Temperature =  30  m(σ) =  0.025390625\n",
      "For Temperature =  10  m(σ) =  0.048828125\n",
      "For Temperature =  5  m(σ) =  0.294921875\n",
      "For Temperature =  2  m(σ) =  1.0\n",
      "For Temperature =  1.5  m(σ) =  1.0\n",
      "For Temperature =  1  m(σ) =  1.0\n",
      "For Temperature =  1.0  m(σ) =  1.0\n",
      "For Temperature =  0.5  m(σ) =  1.0\n",
      "For Temperature =  0.1  m(σ) =  1.0\n",
      "For Temperature =  0.01  m(σ) =  1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question (c)\n",
    "# Parameters\n",
    "L = 32               \n",
    "N           = L * L            \n",
    "nsteps      = N * 100 # I changed the update-rate to 100\n",
    "T           = [30, 10, 5, 2, 1.5, 1, 1.0, 0.5, 0.1, 0.01]\n",
    "M           = []\n",
    "\n",
    "for Temperature in T:\n",
    "    # Local Variables\n",
    "    sum = 0\n",
    "    # Initialize Variables\n",
    "    spins  = np.matlib.ones((L,L))  \n",
    "    kernel = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]])\n",
    "\n",
    "    for n in range(nsteps):\n",
    "        r, c = np.random.randint(0, L, 2)                  # select a vertex (row, column) at random\n",
    "        # indices of a box around r, c\n",
    "        C = [(c-1) % L, c % L, (c + 1) % L]                # periodic boundary conditions, i.e. (0,x) is a neighbour of (L-1,x) \n",
    "        R = [[(r-1) % L], [r % L], [(r+1) % L]]\n",
    "        DH = spins[r, c] * np.sum(kernel * spins[R, C])    \n",
    "        if np.random.rand() < np.exp(- DH / Temperature):  \n",
    "            spins[r, c] *= -1  # flip spin \n",
    "    for i in range(L):\n",
    "        for j in range(L):\n",
    "            sum += spins[i,j]\n",
    "    m = sum/N\n",
    "    M.append(m)\n",
    "    print(\"For Temperature = \",Temperature,\" m(σ) = \",m)\n",
    "\n",
    "# Plotting\n",
    "plt.plot(T,M, label='Temp - Magn')\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('Magn')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pAYa1JDXAsJakBhjWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUAMNakhpgWEtSAwxrSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIaYFhLUgMMa0lqgGEtSQ0wrCWpAdOGdZLlSa5JsjbJ7UlO6qfvkeSqJHf2P3ef/3IlaWka5cj6SeAjVfVK4HXAB5O8CjgZuLqqDgKu7h9LkubBtGFdVRuq6qb+/iPAWmBf4Ghgdd9sNXDMfBUpSUvdNo1ZJ1kBvAa4Hti7qjZAF+jAXnNdnCSpM3JYJ9kZuBj4UFU9vA3LrUqyJsma8fHxmdQoSUveSGGdZAe6oD6vqi7pJ29Msk8/fx9g02TLVtVZVbWyqlaOjY3NRc2StOSMcjVIgHOAtVV1+sCsy4ET+vsnAJfNfXmSJIBlI7R5PfAe4NtJbu6nfRQ4DbgwyfuAHwDvnJ8SJUnThnVVXQdkyOw3z205kqTJ+AlGSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIaYFhLUgMMa0lqgGEtSQ0wrCWpAYa1JDXAsJakBhjWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUAMNakhpgWEtSAwxrSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIaYFhLUgMMa0lqgGEtSQ0wrCWpAYa1JDXAsJakBhjWktQAw1qSGmBYS1IDDGtJaoBhLUkNmDaskyxPck2StUluT3JSP/2UJPcmubm/vW3+y5WkpWnZCG2eBD5SVTcl2QW4MclV/bwzqurT81eeJAlGCOuq2gBs6O8/kmQtsO98FyZJ+pltGrNOsgJ4DXB9P+nEJLcmOTfJ7nNcmySpN3JYJ9kZuBj4UFU9DJwJHAgcQnfk/Zkhy61KsibJmvHx8TkoWZKWnpHCOskOdEF9XlVdAlBVG6vqqap6GjgbOGyyZavqrKpaWVUrx8bG5qpuSVpSRrkaJMA5wNqqOn1g+j4DzY4Fbpv78iRJMNrVIK8H3gN8O8nN/bSPAsclOQQoYB3w/nmpUJI00tUg1wGZZNYVc1+OJGkyfoJRkhpgWEtSAwxrSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIaYFhLUgMMa0lqgGEtSQ0wrCWpAYa1JDXAsJakBhjWktQAw1qSGmBYS1IDDGtJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUAMNakhpgWEtSAwxrSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ADDWpIaYFhLUgMMa0lqgGEtSQ0wrCWpAYa1JDXAsJakBhjWktQAw1qSGmBYS1IDpg3rJDsm+ecktyS5Pcmp/fSXJrk+yZ1JvpLkBfNfriQtTaMcWT8OvKmqDgYOAY5K8jrgz4Azquog4CHgffNXpiQtbdOGdXW29A936G8FvAm4qJ++GjhmXiqUJI02Zp1k+yQ3A5uAq4DvA5ur6sm+yXpg3/kpUZI0UlhX1VNVdQiwH3AY8MrJmk22bJJVSdYkWTM+Pj7zSiVpCdumq0GqajPwTeB1wG5JlvWz9gPuG7LMWVW1sqpWjo2NzaZWSVqyRrkaZCzJbv39nYAjgLXANcA7+mYnAJfNV5GStNQtm74J+wCrk2xPF+4XVtXfJLkDuCDJnwL/Apwzj3VK0pI2bVhX1a3AayaZfhfd+LUkaZ75CUZJaoBhLUkNMKwlqQGGtSQ1wLCWpAYY1pLUAMNakhpgWEtSAwxrSWqAYS1JDUjVpN9sOj8bS8aBuydM3hN44DkrYn7Zl8XJvixO9qVzQFVN+5Wkz2lYT1pAsqaqVi5oEXPEvixO9mVxsi/bxmEQSWqAYS1JDVgMYX3WQhcwh+zL4mRfFif7sg0WfMxakjS9xXBkLUmaxoKGdZKjkvxrku8lOXkha5mtJOuSfDvJzUnWLHQ92yLJuUk2JbltYNoeSa5Kcmf/c/eFrHFUQ/pySpJ7+31zc5K3LWSNo0iyPMk1SdYmuT3JSf305vbLFH1pcb/smOSfk9zS9+XUfvpLk1zf75evJHnBnG97oYZB+v/p+F3gSGA9cANwXFXdsSAFzVKSdcDKqmruutEkbwC2AF+qqlf30z4FPFhVp/UvpLtX1f9cyDpHMaQvpwBbqurTC1nbtkiyD7BPVd2UZBfgRuAY4L00tl+m6Mu7aG+/BHhRVW1JsgNwHXAS8GHgkqq6IMkXgFuq6sy53PZCHlkfBnyvqu6qqieAC4CjF7CeJauqrgUenDD5aGB1f3813ZNr0RvSl+ZU1Yaquqm//wiwFtiXBvfLFH1pTnW29A936G8FvAm4qJ8+L/tlIcN6X+CegcfraXQH9gq4MsmNSVYtdDFzYO+q2gDdkw3Ya4Hrma0Tk9zaD5Ms+qGDQUlW0P3T6utpfL9M6As0uF+SbJ/kZmATcBXwfWBzVT3ZN5mXLFvIsM4k01q+NOX1VXUo8Fbgg/3bcS0OZwIHAocAG4DPLGw5o0uyM3Ax8KGqenih65mNSfrS5H6pqqeq6hBgP7oRgldO1myut7uQYb0eWD7weD/gvgWqZdaq6r7+5ybgUrqd2LKN/Vjj1jHHTQtcz4xV1cb+CfY0cDaN7Jt+TPRi4LyquqSf3OR+mawvre6XrapqM/BN4HXAbkmW9bPmJcsWMqxvAA7qz6K+AHg3cPkC1jNjSV7UnzghyYuAtwC3Tb3Uonc5cEJ//wTgsgWsZVa2hlvvWBrYN/2JrHOAtVV1+sCs5vbLsL40ul/GkuzW398JOIJuDP4a4B19s3nZLwv6oZj+Up3PAtsD51bVJxesmFlI8jK6o2mAZcCXW+pLkvOBN9J9c9hG4OPAV4ELgf2BHwDvrKpFf+JuSF/eSPdWu4B1wPu3jvsuVkkOB74FfBt4up/8Ubqx3qb2yxR9OY729suv0J1A3J7uYPfCqvpEnwEXAHsA/wIcX1WPz+m2/QSjJC1+foJRkhpgWEtSAwxrSWqAYS1JDTCsJakBhrUkNcCwlqQGGNaS1ID/D3mgdhldDR2SAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question (d)\n",
    "# Parameters\n",
    "L = 32               \n",
    "N = L * L            \n",
    "T = 0.01\n",
    "I = [10, 20, 50, 100, 200, 400 ,800]\n",
    "\n",
    "for i in I:\n",
    "    # Local Variables\n",
    "    nsteps = N * i                                         # update-rate = i\n",
    "    # Initialize Variables\n",
    "    spins  = 2 * (np.random.rand(L, L) > 0.5) - 1  \n",
    "    kernel = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]])\n",
    "\n",
    "    for n in range(nsteps):\n",
    "        r, c = np.random.randint(0, L, 2)                  # select a vertex (row, column) at random\n",
    "        # indices of a box around r, c\n",
    "        C = [(c-1) % L, c % L, (c + 1) % L]                # periodic boundary conditions, i.e. (0,x) is a neighbour of (L-1,x) \n",
    "        R = [[(r-1) % L], [r % L], [(r+1) % L]]\n",
    "        DH = spins[r, c] * np.sum(kernel * spins[R, C])    \n",
    "        if np.random.rand() < np.exp(- DH / Temperature):  \n",
    "            spins[r, c] *= -1                              # flip spin \n",
    "    # Plotting\n",
    "    plt.imshow(spins, cmap='binary', vmin=-1, vmax=1, interpolation='nearest')\n",
    "    plt.title(\"Temperature: %.1f, Grid Size: %d\" % (Temperature, L))\n",
    "    plt.show()"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}