CS166 - A simple Ising model simulation

Simple_Ising_Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Ising Model\n",
    "Here we implement a simulation of the Ising model. We run and observe the state of your simulation for temperatures $T = 1, 2, 3, 4, 5$.\n",
    "\n",
    "For small values of $T$, we get states that are completely uniform, corresponding to a low-temperature, strongly magnetized material.\n",
    "\n",
    "For each of the $T$ values above, we plot a histogram over the average magnetization of the final state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "class Ising:\n",
    "\n",
    "    def __init__(self, size=10, temp = 1):\n",
    "        self.size = size\n",
    "        self.temp = temp\n",
    "        self.time_step = 0\n",
    "        self.state = 2*np.random.randint(2, size=(self.size,self.size))-1\n",
    "        self.magnetization = self.state.sum()/(self.size**2)\n",
    "        \n",
    "    def update(self):\n",
    "        n = self.size\n",
    "        for x in range(n):\n",
    "            for y in range(n):            \n",
    "                i, j = np.random.randint(0, self.size), np.random.randint(0, self.size)\n",
    "                s_ij =  self.state[i, j]\n",
    "                sum_s = self.state[(i+1)%n,j] + self.state[i,(j+1)%n] + self.state[(i-1)%n,j] + self.state[i,(j-1)%n]\n",
    "                exp_factor = -2*s_ij*sum_s/self.temp\n",
    "\n",
    "                flip_prob = np.exp(exp_factor)\n",
    "                \n",
    "                if flip_prob >= 1 or np.random.random() < flip_prob:\n",
    "                    s_ij *= -1\n",
    "                self.state[i, j] = s_ij\n",
    "                \n",
    "        self.magnetization = self.state.sum()/(self.size**2)\n",
    "        self.time_step += 1\n",
    "        \n",
    "    def simulate(self, n_steps = 10):\n",
    "        for step in range(n_steps):\n",
    "            self.update()\n",
    "        return self.magnetization\n",
    "\n",
    "    def draw(self):\n",
    "        plt.cla()\n",
    "        plt.pcolor(self.state, vmin = 0, vmax = 1, cmap = plt.cm.binary)\n",
    "        plt.axis('image')\n",
    "        plt.title('t = ' + str(self.time_step))\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "n_steps = 1000\n",
    "\n",
    "sim = Ising(size = 50, temp = 1)\n",
    "for i in range(n_steps):\n",
    "    sim.update()\n",
    "    if i in [0, n_steps // 10 - 1, n_steps-1]:\n",
    "        sim.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ts = list(range(1, 6))\n",
    "n_trials = 100\n",
    "\n",
    "dists = [[] for _ in range(len(Ts))]\n",
    "\n",
    "for T in Ts:\n",
    "    for trial in range(n_trials):\n",
    "        sim = Ising(temp = T)\n",
    "        dists[T-1].append(sim.simulate(n_steps = 100))"
   ]
  },
  {
   "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "for dist in dists:\n",
    "    plt.hist(dist)\n",
    "    plt.title(f'Histogram of average system magnetization at 100th step for T = {dists.index(dist)+1}')\n",
    "    plt.ylabel('Count')\n",
    "    plt.xlabel('Average magnetization')\n",
    "    plt.xlim((-1,1))\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": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}