tomkreker · March 29, 2020 11:33
diff --git a/cs166-12.1-pcw.ipynb b/cs166-12.1-pcw.ipynb
 {
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class MagnetSimulation:\n",
    "    \n",
    "    def __init__(self,N,T):\n",
    "        self.N = N\n",
    "        self.T=T\n",
    "        self.state=np.ones((N,N))\n",
    "        self.time=0\n",
    "        \n",
    "    def initialize(self):\n",
    "        # initialize the grid to either 1 or -1 randomly\n",
    "        for i in range(self.N):\n",
    "            for j in range(self.N):\n",
    "                if np.random.random() < 0.5:\n",
    "                    self.state[i,j] = -1\n",
    "    def observe(self):\n",
    "        plt.pcolormesh(self.state, cmap = plt.cm.binary)\n",
    "        plt.xticks(range(self.N))\n",
    "        plt.yticks(range(self.N))\n",
    "        plt.show()\n",
    "    \n",
    "    def update(self):\n",
    "        i,j = np.random.randint(0,self.N,size=2)\n",
    "        E=0\n",
    "        for dy in [-1,1]: #row neighbors\n",
    "            E+= self.state[i, ((j+dy)+self.N)%self.N]\n",
    "        for dx in [-1,1]: #column neighbors\n",
    "            E+= self.state[((i+dx)+self.N)%self.N, j]\n",
    "        E = E * -self.state[i,j]\n",
    "        p_flip = np.exp(2*E/self.T)\n",
    "        if np.random.random() < p_flip:\n",
    "            self.state[i,j] = -self.state[i,j]\n",
    "    \n",
    "    def get_magnetism(self):\n",
    "        return np.sum(self.state)/(self.N**2)\n",
    "        \n",
    "        #if synchronus (I was happy with this until realized it's only needed for a cell)\n",
    "        #Ematrix = np.zeros((self.N,self.N))\n",
    "        #for dx in [-1,1]:\n",
    "        #    shift_row = np.roll(self.state, shift=dx, axis=1)\n",
    "        #    for dy in [-1,1]:\n",
    "        #        shift_col = np.roll(shift_row, shift=dy, axis=0)\n",
    "        #        Ematrix+=shift_col\n",
    "        #Ematrix=np.multiply(-self.state,Ematrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run simulations for different T values\n",
    "Ts = [1,2,3,4,5]\n",
    "num_steps = 100000\n",
    "num_sims = 100\n",
    "results = np.zeros((len(Ts),num_sims))\n",
    "for i in range(len(Ts)):\n",
    "    for j in range(num_sims):\n",
    "        sim = MagnetSimulation(N=10,T=Ts[i])\n",
    "        sim.initialize()\n",
    "        for k in range(num_steps):\n",
    "            sim.update()\n",
    "        results[i,j]=sim.get_magnetism()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x260bfaa61d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x260bf7bdc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x260bf9d19e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x260bf722128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Rzho6E/gd4P4kO7q2/wSsB6iqa4CLgXckOQD8ELikqmqEMSVJYzZ0EFTVHUBW6HM1cPWw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x260bf781390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot histogram for each T value\n",
    "\n",
    "for i in range(len(Ts)):\n",
    "    plt.hist(results[i])\n",
    "    plt.title('T={}'.format(Ts[i]))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are as expected, since low values of T were expected to be uniform so either close to -1 or 1 whereas higher values of T were expected to be random, so values towards the center."
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
 }
No results found