MC-2D-Solution (2).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "import time\n",
    "\n",
    "def init(N,L):\n",
    "    \"\"\"returns a list of N occupied sites and an LxL lattice with 0's for\n",
    "       empty sites and integers >0 corresponding to non-empty sites. \"\"\"\n",
    "    lattice = numpy.zeros((L,L),dtype=numpy.int8)#Initialize empty lattice\n",
    "    occupied = numpy.random.choice(L*L,N,replace=False)\n",
    "    for i,site in enumerate(occupied):\n",
    "        lattice[site//L][site%L] = i+1 #convert index on [0,V**2) to [0,V)[0,V)\n",
    "    return occupied, lattice\n",
    "        \n",
    "def adjacent(site,L):\n",
    "    \"\"\"Return a tuple with indices corresponding to the four sites adjacent\n",
    "       to the one passed in, wrapping around a LxL periodic volume.\"\"\"\n",
    "    row = site//L\n",
    "    col = site%L\n",
    "    left = ((col - 1 + L) % L) + row*L\n",
    "    right = ((col + 1) % L) + row*L\n",
    "    up =  ((row - 1 + L) % L)*L + col\n",
    "    down =  ((row + 1) % L)*L + col\n",
    "    return (right, down, up, left)\n",
    "    \n",
    "def energy(occupied,lattice,epsilon=-1):\n",
    "    \"\"\"Returns the total potential energy for the occupied sites on a lattice.\"\"\"\n",
    "    U = 0\n",
    "    L = len(lattice)\n",
    "    for site in occupied: #loop over all sites\n",
    "        for neighbor in adjacent(site,L)[:2]: #Look right and down so we  don't double count\n",
    "            if lattice[neighbor//L][neighbor%L] != 0:\n",
    "                U+=epsilon\n",
    "    return U\n",
    "\n",
    "def trial_move(occupied,lattice,T):\n",
    "    L=len(lattice)\n",
    "    V = L*L\n",
    "    Uo = energy(occupied,lattice)\n",
    "    numpy.random.shuffle(occupied) #shuffles the elements of occupied\n",
    "    old = occupied[0]\n",
    "    empty_mask = numpy.isin(numpy.arange(V),occupied,invert=True)\n",
    "    empty_sites = numpy.arange(V)[empty_mask] # list of empty sites\n",
    "    new = empty_sites[numpy.random.randint(len(empty_sites))]\n",
    "    occupied[0]= new\n",
    "    lattice[new//L][new%L] = lattice[old//L][old%L]\n",
    "    lattice[old//L][old%L] = 0\n",
    "    Un = energy(occupied,lattice)\n",
    "    if (Un<=Uo) or numpy.random.random() < numpy.exp(-(Un-Uo)/T):\n",
    "        return occupied, lattice, Un\n",
    "    lattice[old//L][old%L] = lattice[new//L][new%L]\n",
    "    lattice[new//L][new%L] = 0\n",
    "    occupied[0]=old\n",
    "    return occupied, lattice, Uo\n",
    "\n",
    "def run(nsteps,T,occupied, lattice):\n",
    "    U = []\n",
    "    for step in range(int(nsteps)):\n",
    "        occupied, lattice, u = trial_move(occupied, lattice,T)\n",
    "        U.append(u)\n",
    "    return numpy.array(U)/len(occupied)\n",
    "\n",
    "def analyze(data):\n",
    "    a = numpy.average(data)\n",
    "    s = numpy.std(data)\n",
    "    return a,s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n",
      "20\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n",
      "30\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n",
      "40\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n",
      "50\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n",
      "60\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n",
      "70\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n",
      "80\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n",
      "90\n",
      "\t 0.1\n",
      "\t 0.2\n",
      "\t 0.30000000000000004\n",
      "\t 0.4\n",
      "\t 0.5\n",
      "\t 0.6\n",
      "\t 0.7000000000000001\n",
      "\t 0.8\n",
      "\t 0.9\n",
      "\t 1.0\n",
      "\t 1.1\n",
      "\t 1.2000000000000002\n",
      "\t 1.3000000000000003\n",
      "\t 1.4000000000000001\n",
      "\t 1.5000000000000002\n",
      "\t 1.6\n",
      "\t 1.7000000000000002\n",
      "\t 1.8000000000000003\n",
      "\t 1.9000000000000001\n"
     ]
    }
   ],
   "source": [
    "Temps = numpy.arange(0.1,2.,0.1)\n",
    "Sizes = range(10,100,10)\n",
    "results = {}\n",
    "for N in Sizes:\n",
    "    print(N)\n",
    "    onerun = []\n",
    "    for T in Temps:\n",
    "        print(\"\\t\",T)\n",
    "        occupied, lattice = init(N,10) # N, L\n",
    "        start = time.time()\n",
    "        U = run(1e3,T,occupied, lattice)\n",
    "        a, s = analyze(U)\n",
    "        finish = time.time()\n",
    "        onerun.append((a,s,finish-start))\n",
    "        results[N] =  numpy.array(onerun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '<Seconds>')"
      ]
     },
     "execution_count": 4,
     "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": [
    "times = []\n",
    "for N in Sizes:\n",
    "    times.append((numpy.average(results[N][:,2]),numpy.std(results[N][:,2])))\n",
    "times = numpy.array(times)\n",
    "plt.errorbar(Sizes,times[:,0],times[:,1])\n",
    "plt.xlabel(\"N\")\n",
    "plt.ylabel(\"<Seconds>\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '<U>')"
      ]
     },
     "execution_count": 5,
     "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": [
    "plt.errorbar(Temps,results[10][:,0],results[20][:,1])\n",
    "plt.errorbar(Temps,results[50][:,0],results[20][:,1])\n",
    "plt.errorbar(Temps,results[90][:,0],results[20][:,1])\n",
    "plt.xlabel(\"T\")\n",
    "plt.ylabel(\"<U>\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.01975309, -0.01975309, -0.01975309, -0.01987654, -0.01987654,\n",
       "       -0.01987654, -0.01987654, -0.01975309, -0.01987654, -0.01987654,\n",
       "       -0.01987654, -0.01987654, -0.01987654, -0.01987654, -0.01987654,\n",
       "       -0.01975309, -0.02      , -0.02      , -0.02      , -0.02012346,\n",
       "       -0.02012346, -0.02012346, -0.02012346, -0.02024691, -0.02012346,\n",
       "       -0.02012346, -0.02012346, -0.02      , -0.01987654, -0.01987654,\n",
       "       -0.01987654, -0.01987654, -0.01987654, -0.01987654, -0.01987654,\n",
       "       -0.02      , -0.02      , -0.02      , -0.02012346, -0.02012346,\n",
       "       -0.02012346, -0.02012346, -0.02012346, -0.02012346, -0.02012346,\n",
       "       -0.02      , -0.02      , -0.02      , -0.02      , -0.02      ,\n",
       "       -0.01987654, -0.02      , -0.02      , -0.02012346, -0.02012346,\n",
       "       -0.02      , -0.02012346, -0.02      , -0.01987654, -0.01987654,\n",
       "       -0.02      , -0.02      , -0.02      , -0.02      , -0.02      ,\n",
       "       -0.01987654, -0.01987654, -0.01987654, -0.01987654, -0.01987654,\n",
       "       -0.01987654, -0.01975309, -0.01987654, -0.01987654, -0.01975309,\n",
       "       -0.01975309, -0.01975309, -0.01975309, -0.01975309, -0.01987654,\n",
       "       -0.01987654, -0.01987654, -0.01987654, -0.02      , -0.02012346,\n",
       "       -0.02      , -0.02      , -0.01987654, -0.02      , -0.02012346,\n",
       "       -0.02024691, -0.02037037, -0.02012346, -0.02012346, -0.02      ,\n",
       "       -0.02      , -0.02      , -0.02012346, -0.02012346, -0.02012346,\n",
       "       -0.02012346, -0.02      , -0.02      , -0.02012346, -0.02012346,\n",
       "       -0.02012346, -0.02012346, -0.02012346, -0.02024691, -0.02012346,\n",
       "       -0.02012346, -0.02      , -0.02012346, -0.02012346, -0.02012346,\n",
       "       -0.02012346, -0.02012346, -0.02012346, -0.02012346, -0.02012346,\n",
       "       -0.02012346, -0.02012346, -0.02012346, -0.02012346, -0.02012346,\n",
       "       -0.02012346, -0.02012346, -0.02012346, -0.02012346, -0.02012346,\n",
       "       -0.02012346, -0.02024691, -0.02024691, -0.02037037, -0.02037037,\n",
       "       -0.02037037, -0.02024691, -0.02024691, -0.02012346, -0.02024691,\n",
       "       -0.02012346, -0.02012346, -0.02012346, -0.02012346, -0.02      ,\n",
       "       -0.02      , -0.02      , -0.02      , -0.02012346, -0.02012346,\n",
       "       -0.02012346, -0.02012346, -0.02024691, -0.02024691, -0.02024691,\n",
       "       -0.02037037, -0.02049383, -0.02037037, -0.02049383, -0.02061728,\n",
       "       -0.02061728, -0.02061728, -0.02061728, -0.02061728, -0.02061728,\n",
       "       -0.02049383, -0.02024691, -0.02024691, -0.02024691, -0.02012346,\n",
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       "       -0.02      , -0.02012346, -0.02012346, -0.02012346, -0.01987654])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U/len(occupied)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(occupied)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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