{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.spatial.distance as spd\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import time\n",
      "# used to compare energy before and after a move\n",
      "# we assumed that epsilon and alpha are 1\n",
      "def local_energy(site):\n",
      "    local_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        if site != i:\n",
      "            dist = spd.euclidean(system[site],system[i])\n",
      "            local_sum += -((1/dist)**12-(1/dist)**6)\n",
      "    return local_sum\n",
      "\n",
      "# total energy of the system\n",
      "def system_energy():\n",
      "    total_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        total_sum += local_energy(i)\n",
      "    return total_sum\n",
      "\n",
      "def radial_number_density():\n",
      "    rad_dist = []\n",
      "    for i in xrange(len(system)):\n",
      "        for j in xrange(len(system)):\n",
      "            if i != j:\n",
      "                temp = spd.euclidean(system[i],system[j])\n",
      "                rad_dist.append(temp)\n",
      "    return rad_dist\n",
      "\n",
      "n = 400 # number of particles\n",
      "# initializing the system\n",
      "# the atoms occupy a square of size 10X10\n",
      "system = np.zeros([n,2])\n",
      "for i in xrange(len(system)):\n",
      "    system[i][0] = i%20 # np.sqrt(n) wont work as it will return a float\n",
      "    system[i][1] = i/20 # we need an integer denominator for this to work!\n",
      "\n",
      "global_energy = []\n",
      "accepted_moves = 0\n",
      "\n",
      "#plt.subplot(131)\n",
      "radial_dist_before = radial_number_density()\n",
      "#anarray = np.asarray(alist)\n",
      "#plt.hist(anarray,10);\n",
      "\n",
      "T = 1.\n",
      "# T = np.array([5.,5./2,1./1./2,1./10])\n",
      "beta = 1./T\n",
      "# B = 1./T\n",
      "#for beta in B:\n",
      "time_per_loop = []\n",
      "for looptime in xrange(1000):\n",
      "    start_time = time.time()\n",
      "    site = np.random.choice(np.arange(n)) # atom to be moved\n",
      "    # this atom can now move in the range (-alpha,alpha) in x & y\n",
      "    #xmove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #ymove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    xmove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    ymove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #xmove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    #ymove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    pre_move_e = local_energy(site)\n",
      "    system[site] = system[site] + np.array([xmove,ymove])\n",
      "    if system[site][0] > 30 :\n",
      "        system[site][0] = system[site][0]%30\n",
      "    #if system[site][0] < 0 :\n",
      "    #    system[site][0] = system[site][0]%100\n",
      "    if system[site][1] > 30 :\n",
      "        system[site][1] = system[site][1]%30\n",
      "    #if system[site][1] < 0 :\n",
      "    #    system[site][1] = system[site][1]%100\n",
      "    post_move_e = local_energy(site)\n",
      "    if post_move_e - pre_move_e < 0:\n",
      "        global_energy.append(system_energy())\n",
      "        accepted_moves += 1\n",
      "        print \"yes\"\n",
      "    else :\n",
      "        temp = np.random.random()\n",
      "        if temp < np.exp(-beta*(post_move_e - pre_move_e)):\n",
      "            global_energy.append(system_energy())\n",
      "            accepted_moves += 1\n",
      "            print \"barely yes\"\n",
      "        else :\n",
      "            system[site] = system[site] - np.array([xmove,ymove])\n",
      "            global_energy.append(system_energy())\n",
      "            print \"nyooo!!!!\"\n",
      "    print \"we're done with the mc loop %f\" % (time.time()-start_time)\n",
      "    time_per_loop.append(time.time()-start_time)\n",
      "# we get global_energy, accepted moves as the outputs here.\n",
      "#plt.subplot(132)\n",
      "radial_dist_after = radial_number_density()\n",
      "#anarray = np.asarray(alist)\n",
      "#plt.hist(anarray,10);\n",
      "#plt.subplot(133)\n",
      "#plt.plot(global_energy)\n",
      "#print \"we're done with plotting routine %f\" % (time.time()-start_time)\n",
      "print \"accepted_moves\", accepted_moves"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "yes\n",
        "we're done with the mc loop 7.540733\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 5.782312\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.439022\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.346425\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.362946\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.817872\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.267065\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.263690\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.274417\n",
        "yes"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.685855\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 5.781334\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.091565\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.281504\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.285362\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.034200\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.252084\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.183772\n",
        "nyooo!!!!"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.729865\n",
        "nyooo!!!!"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 10.021109\n",
        "nyooo!!!!"
       ]
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.070629\n",
        "yes"
       ]
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      {
       "output_type": "stream",
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       "text": [
        "\n",
        "we're done with the mc loop 8.546466\n",
        "yes"
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      {
       "output_type": "stream",
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       "text": [
        "\n",
        "we're done with the mc loop 9.929984\n",
        "yes"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.019647\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 6.440690\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.250816\n",
        "yes"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.843503\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.590732\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.375478\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.636384\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.146533\n",
        "nyooo!!!!"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.345734\n",
        "barely yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.303199\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.370839\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.379156\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.474897\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.271929\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.278001\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.261701\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.279529\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.296288\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.277682\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.296111\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.290898\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.249907\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.270735\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.282030\n",
        "barely yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.250911\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.266958\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.283772\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.276527\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.286787\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.284596\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.275902\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.279064\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 6.729150\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 5.538854\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 5.548928\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.795378\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.136810\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.325426\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.384433\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.286372\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.311450\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.377447\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.402615\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 5.574311\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.485756\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.295956\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 6.257114\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 6.377398\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.294242\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.301500\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.540840\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.336970\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 11.174839\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 10.415587\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 8.874583\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.777362\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.343725\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 10.639781\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.846132\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.724817\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.248298\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.775423\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 10.331786\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 11.369211\n",
        "yes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.375793\n",
        "barely yes"
       ]
      },
      {
       "output_type": "stream",
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        "we're done with the mc loop 13.500123\n",
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       "output_type": "stream",
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       "output_type": "stream",
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        "we're done with the mc loop 10.207865\n",
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        "nyooo!!!!"
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        "we're done with the mc loop 12.826558\n",
        "yes"
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        "we're done with the mc loop 15.312075\n",
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        "we're done with the mc loop 9.872628\n",
        "nyooo!!!!"
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        "we're done with the mc loop 10.259911\n",
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        "we're done with the mc loop 9.162322\n",
        "nyooo!!!!"
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        "we're done with the mc loop 8.544719\n",
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        "we're done with the mc loop 10.321126\n",
        "nyooo!!!!"
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        "we're done with the mc loop 9.201921\n",
        "yes"
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        "we're done with the mc loop 10.539753\n",
        "nyooo!!!!"
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        "we're done with the mc loop 9.486442\n",
        "nyooo!!!!"
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        "nyooo!!!!"
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        "we're done with the mc loop 7.808444\n",
        "yes"
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       "output_type": "stream",
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        "we're done with the mc loop 11.124188\n",
        "yes"
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       "output_type": "stream",
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        "we're done with the mc loop 13.223310\n",
        "yes"
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        "we're done with the mc loop 9.962305\n",
        "yes"
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        "we're done with the mc loop 9.467551\n",
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        "we're done with the mc loop 9.275611\n",
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        "we're done with the mc loop 7.969724\n",
        "yes"
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        "we're done with the mc loop 9.516299\n",
        "yes"
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        "we're done with the mc loop 7.731129\n",
        "yes"
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        "we're done with the mc loop 9.511431\n",
        "yes"
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        "we're done with the mc loop 7.607254\n",
        "yes"
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        "we're done with the mc loop 9.583686\n",
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        "we're done with the mc loop 7.824486\n",
        "yes"
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        "we're done with the mc loop 9.642111\n",
        "nyooo!!!!"
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        "we're done with the mc loop 7.668383\n",
        "yes"
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        "we're done with the mc loop 9.780911\n",
        "yes"
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        "we're done with the mc loop 7.529290\n",
        "nyooo!!!!"
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        "we're done with the mc loop 9.200338\n",
        "yes"
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        "we're done with the mc loop 7.469806\n",
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        "we're done with the mc loop 12.016145\n",
        "nyooo!!!!"
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        "we're done with the mc loop 10.648659\n",
        "nyooo!!!!"
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        "we're done with the mc loop 11.080918\n",
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        "we're done with the mc loop 11.071192\n",
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        "we're done with the mc loop 7.353254\n",
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        "we're done with the mc loop 12.751735\n",
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        "we're done with the mc loop 13.472055\n",
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        "we're done with the mc loop 6.923523\n",
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        "we're done with the mc loop 8.544086\n",
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       "text": [
        "\n",
        "we're done with the mc loop 7.474652\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 7.134204\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 9.808389\n",
        "nyooo!!!!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "we're done with the mc loop 10.796990\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 449\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.subplot(121)\n",
      "anarray = np.asarray(radial_dist_before)\n",
      "plt.hist(anarray,10);\n",
      "plt.subplot(122)\n",
      "anotherarray = np.asarray(radial_dist_after)\n",
      "plt.hist(anotherarray,10);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YORXAxx9/DADo7u6Gw+FAcnIycnNz1b3cAKcCICIKa0973HnkVADJycnS0tIiW7ZskV27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\nRMr/B0PRHOWmir2mAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb4cca44c>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(global_energy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "[<matplotlib.lines.Line2D at 0xaffa160c>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xafe56d0c>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}