ising_model_1d.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This code will simulate the ising model in one dimension using the monte carlo method.\n",
      "\n",
      "Written by Poruri Sai Rahul\n",
      "\n",
      "Added comments on 6 Nov 2014"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Theory\n",
      "=======\n",
      "\n",
      "The ising model is a theoretical model used to understand the interactions of spins and a 1-d ising model, as the name suggests is a system of spins arranged in a 1-dimensional chain or string. There are different kinds of coupling in literature and for the sake of our simulations here, we will only look at the nearest neighbor interaction i.e any spin in the string can only interact with it's neighbors on the left and the right. The hamiltonian of the system can be written as \n",
      "\n",
      "$$H = \\Sigma_{i!=j} J_{i,j} S_i S_j$$\n",
      "\n",
      "where J is the strength of the interaction between adjacent spins. One other assumption we make in our simulations is that the spins are discrete and not continuous i.e the spins can only take values +1 or -1 or pointing upwards or downwards. We also assume that the interaction term $J_{i,j}$ is the same for all spins, making the hamiltonian\n",
      "\n",
      "$$H = J \\Sigma_{i!=j} S_i S_j$$\n",
      "\n",
      "The following simulations study the equilibrium conditions of a 1-dim ising model of various sizes and at various temperatures. The equilibrium conditions of the model are arrived at using monte carlo simulations. In a a monte carlo (mc hereforth) of the ising model, we choose a spin site randomly from the string of spins and flip it. Well, we choose to flip it with a probability depending on the energy of the post-flip state. Assuming we flip the spin, we measure the energy of the post-flip state. If the flip will decrease the energy of the system, then we probability of the flip is 1. Otherwise, the probability of the flip is $exp(-\\beta \\Delta E)$ where $\\beta$ is $1/k_bT$ and $\\Delta E$ is the change in energy before and after flip.b"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Code\n",
      "=====\n",
      "\n",
      "There are multiple instances of monte carlo code below. The first one is a preliminary look at how the system energy and magnetization change over monte carlo steps for various values of temperature. The second one repeats the first step increasing the number of monte carlo iterations and making the use of monte carlo sweep to measure system energy and system magnetization for fewer instances. We also measure the auto-correlation function of magnetization here. Finally, we look at how the system size itself will manifest as change in average value of magnetization and in the auto-correlation function of the same.\n",
      "\n",
      "*NOTE: The average value of magnetization isnt zero, as it is supposed to be and the auto-correlation function is giving negative values, which doesnt make sense! need to debug!*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Structure\n",
      "======\n",
      "\n",
      "We first initialize the lattice or system, either with uniform spins or random spins. We have defined functions that take lattice as input and measure the system energy & magnetization. And then we have the main monte carlo loop where we choose a spin from the lattice and see what the probability of flipping it is, depending on what the post flip energy is. At the end of the mc loop, we also measured the auto-correlation function of magnetization."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#lattice = np.ones(200) # initializing a uniform lattice\n",
      "lattice = np.zeros(200) # initializing a random lattice\n",
      "for i in xrange(200):\n",
      "    temp = np.random.random()\n",
      "    if temp > 1./2:\n",
      "        lattice[i] = 1\n",
      "    else :\n",
      "        lattice[i] = -1\n",
      "\n",
      "# function that initializes a lattice of size i with random values\n",
      "def initialize(i):\n",
      "    lattice = np.zeros(i)\n",
      "    for i in xrange(len(lattice)):\n",
      "        temp = np.random.random()\n",
      "        if temp > 1./2:\n",
      "            lattice[i] = +1\n",
      "        if temp < 1./2:\n",
      "            lattice[i] = -1\n",
      "    \n",
      "# defines the local energy i.e product of neighbor spins.\n",
      "# used to compare the change in energy before and after a flip\n",
      "# the boundary condition is that the 0th spin is coupled to the nth spin\n",
      "def energy_local(site):\n",
      "    if site == 0:\n",
      "        return lattice[0]*lattice[1] - lattice[0]*lattice[-1]\n",
      "    # we dont actually need to specify the condition for 0 because in numpy arrays\n",
      "    # array[-1] is the same as array[n-1] where n is the length of the array.\n",
      "    elif site == len(lattice)-1 :\n",
      "        return lattice[len(lattice)-1]*lattice[len(lattice)-2] - lattice[len(lattice)-1]*lattice[0]\n",
      "    else :\n",
      "        return lattice[site]*lattice[site-1] - lattice[site]*lattice[site+1]\n",
      "\n",
      "# computes the total energy of the system i.e sum of products of all spins\n",
      "# assuming J = 1 and nearest neighbor coupling\n",
      "def global_energy():\n",
      "    temp = 0\n",
      "    for i in xrange(len(lattice)-1):\n",
      "        temp += -(lattice[i-1]*lattice[i]+lattice[i]*lattice[i+1])\n",
      "    return (1./2)*temp/len(lattice)\n",
      "\n",
      "# computing the total magnetization i.e the sum of all spins in the lattice\n",
      "def global_magnetization():\n",
      "    return np.sum(lattice)/len(lattice)\n",
      "\n",
      "T = np.array([5,5./2,1,1./2,2./10])\n",
      "betaJ = 1./T\n",
      "# we intend to study the system behavior at different temperatures\n",
      "# therefore, we keep J constant at 1 and scale the value of $\\beta$ as that of $1./T$\n",
      "for bJ in betaJ:\n",
      "    plt.hold(True)\n",
      "    plt.legend(loc='upper center')\n",
      "    global_e = []\n",
      "    global_e.append(global_energy())                         # the initial system energy\n",
      "    magnetization = []\n",
      "    magnetization.append(global_magnetization())             # the initial system magnetization\n",
      "    accepted_moves = 0\n",
      "    for i in xrange(50000):\n",
      "        site = np.random.choice(np.linspace(0,199,200))      # choose a site randomly from the lattice\n",
      "        pre_flip_e = energy_local(site)                      # compute local energy before flip\n",
      "        lattice[site] = -lattice[site]  \n",
      "        post_flip_e = energy_local(site)                     # compute local energy after flip\n",
      "        if post_flip_e - pre_flip_e < 0:\n",
      "            global_e.append(global_energy())                 # update the system energy at this step\n",
      "            accepted_moves += 1\n",
      "            magnetization.append(global_magnetization())     # update the system magnetization at this step\n",
      "        else :\n",
      "            temp = np.random.random()\n",
      "            if temp < np.exp(-bJ*(post_flip_e - pre_flip_e)):\n",
      "                global_e.append(global_energy())\n",
      "                accepted_moves += 1\n",
      "                magnetization.append(global_magnetization())\n",
      "            else :\n",
      "                lattice[site] = -lattice[site]               # reverse the flip to initial state if the transition isnt valid\n",
      "                global_e.append(global_energy())\n",
      "                magnetization.append(global_magnetization())\n",
      "    print \"accepted_moves\", accepted_moves, \"temperature\", 1./bJ\n",
      "    plt.subplot(121)\n",
      "    plt.plot(global_e,label=1./bJ)\n",
      "    plt.subplot(122)\n",
      "    plt.plot(magnetization,label=1./bJ)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "accepted_moves 40025 temperature 5.0\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 30828 temperature 2.5\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11615 temperature 1.0\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3051 temperature 0.5\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1822 temperature 0.2\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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i423atMGvdHD/2267DRaXPhDB4LZavNAfQNo3wPfCqGoCxuAqgupK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\n0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3YfeOABPPvss7BxCXLq6n5LkoTrrrsOvXr1wptvvlmnbbuDS2ls1/W4BnDZje1AG9f1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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb04c292c>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "splitting mcsteps into mcsweep\n",
      "===="
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#lattice = np.ones(200) # initializing the lattice with all ones\n",
      "lattice = np.zeros(200) # initializing the lattice randomly\n",
      "for i in xrange(200):\n",
      "    temp = np.random.random()\n",
      "    if temp > 1./2:\n",
      "        lattice[i] = 1\n",
      "    else :\n",
      "        lattice[i] = -1\n",
      "\n",
      "# defines the local energy i.e product of neighbor spins.\n",
      "# used to compare the change in energy before and after a flip\n",
      "# with the boundary condition that the 0th spin is coupled to the nth spin\n",
      "def energy_local(site):\n",
      "    if site == 0:\n",
      "        return - lattice[0]*lattice[1] - lattice[0]*lattice[-1]\n",
      "    elif site == len(lattice)-1 :\n",
      "        return - lattice[len(lattice)-1]*lattice[len(lattice)-2] - lattice[len(lattice)-1]*lattice[0]\n",
      "    else :\n",
      "        return - lattice[site]*lattice[site-1] - lattice[site]*lattice[site+1]\n",
      "\n",
      "# computes the total energy of the system i.e sum of products of all spins\n",
      "# assuming J = 1\n",
      "def global_energy():\n",
      "    temp = 0\n",
      "    for i in xrange(len(lattice)-1):\n",
      "        temp += -(lattice[i-1]*lattice[i]+lattice[i]*lattice[i+1])\n",
      "    return (1./2)*temp/len(lattice)\n",
      "\n",
      "# computing the total magnetization i.e the sum of all spins in the lattice\n",
      "def global_magnetization():\n",
      "    return np.sum(lattice)/len(lattice)\n",
      "\n",
      "T = np.array([5,5./2,1,1./2,2./10])\n",
      "betaJ = 1./T\n",
      "for bJ in betaJ:\n",
      "    plt.hold(True)\n",
      "    plt.legend(loc='upper center')\n",
      "    global_e = []\n",
      "    global_e.append(global_energy())                             # the initial system energy\n",
      "    magnetization = []\n",
      "    magnetization.append(global_magnetization())                 # the initial system magnetization\n",
      "    accepted_moves = 0\n",
      "    for step in xrange(1000):\n",
      "        for mcsweep in xrange(200):                              # an mcsweep is the n number of iterations, n = system size\n",
      "            site = np.random.choice(np.linspace(0,199,200))      # choose a site randomly from the lattice\n",
      "            pre_flip_e = energy_local(site)                      # compute local energy before flip\n",
      "            lattice[site] = -lattice[site]  \n",
      "            post_flip_e = energy_local(site)                     # compute local energy after flip\n",
      "            if post_flip_e - pre_flip_e < 0:\n",
      "    #            global_e.append(global_energy())                # update the system energy at this step\n",
      "                accepted_moves += 1\n",
      "    #            magnetization.append(global_magnetization())    # update the system magnetization at this step\n",
      "            else :\n",
      "                temp = np.random.random()\n",
      "                if temp < np.exp(-bJ*(post_flip_e - pre_flip_e)):\n",
      "    #                global_e.append(global_energy())\n",
      "                    accepted_moves += 1\n",
      "    #                magnetization.append(global_magnetization())\n",
      "                else :\n",
      "                    lattice[site] = -lattice[site]               # reverse the flip to initial state if the transition isnt valid\n",
      "    #                global_e.append(global_energy())\n",
      "    #                magnetization.append(global_magnetization())\n",
      "        global_e.append(global_energy())\n",
      "        magnetization.append(global_magnetization())\n",
      "    print \"accepted_moves\", accepted_moves, \"temperature\", 1./bJ\n",
      "    plt.subplot(131)\n",
      "    plt.plot(global_e,label=1./bJ)\n",
      "    plt.subplot(132)\n",
      "    plt.plot(magnetization,label=1./bJ)\n",
      "    # to plot the auto-correlation function using magnetization\n",
      "    tmax = len(magnetization) # the total number of iterations\n",
      "    chi = []\n",
      "    for t in xrange(1,100): # the upper limit of the range should be ~1/2 of that of tmax!\n",
      "        # first term in the equation\n",
      "        temp = 0\n",
      "        for tprime in xrange(tmax-t):\n",
      "            temp += magnetization[tprime]*magnetization[tprime+t]\n",
      "        temp = (1./(tmax-t))*temp\n",
      "        # second term in the equation\n",
      "        # it was mentioned that this second term is not necessary.\n",
      "        # it is a correction for mean value!\n",
      "        temp1 = 0\n",
      "        for tprime in xrange(tmax-t):\n",
      "            temp1 += magnetization[tprime]\n",
      "        temp2 = 0\n",
      "        for tprime in xrange(tmax-t):\n",
      "            temp2 += magnetization[tprime+t]\n",
      "        tempo = (1./((tmax-t)**2))*temp1*temp2\n",
      "        # auto-correlation function value\n",
      "        chi.append(temp-tempo)\n",
      "    plt.subplot(133)\n",
      "    plt.plot(chi,label=1./bJ)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(magnetization,label=1./bJ)\n",
      "plt.legend(loc='upper right')\n",
      "#plt.xticks([])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.legend.Legend at 0xb13acd8c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GQ4bQVnTIepKZSVHLzhCdZkeH/m04dYqsHmU+JW8Gt910Ey2pjYtz3vkvX+69djAM49/4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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb13ac06c>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#t = 10 # we need to iterate over this \n",
      "tmax = len(magnetization) # the total number of iterations\n",
      "chi = []\n",
      "import time\n",
      "start_time = time.time()\n",
      "for t in xrange(1,100): # the upper limit of the range should be ~1/2 of that of tmax!\n",
      "    # first term in the equation\n",
      "    temp = 0\n",
      "    for tprime in xrange(tmax-t):\n",
      "        temp += magnetization[tprime]*magnetization[tprime+t]\n",
      "    temp = (1./(tmax-t))*temp\n",
      "    # second term in the equation\n",
      "    temp1 = 0\n",
      "    for tprime in xrange(tmax-t):\n",
      "        temp1 += magnetization[tprime]\n",
      "    temp2 = 0\n",
      "    for tprime in xrange(tmax-t):\n",
      "        temp2 += magnetization[tprime+t]\n",
      "    tempo = (1./((tmax-t)**2))*temp1*temp2\n",
      "    chi.append(temp-tempo)\n",
      "plt.plot(np.asarray(chi)-110,label='old method')\n",
      "print time.time()-start_time"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.316520929337\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3gfrLX+xyJLGxdhvaQB5tpaQhItJOMTHw6KN2qO7gwXa4bnJyYG5DqxnhIiId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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb135fc4c>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# two different ways to measure the auto-correlation function\n",
      "# first way by summing elements using for loops\n",
      "#t = 10 # we need to iterate over this \n",
      "tmax = len(magnetization) # the total number of iterations\n",
      "chi = []\n",
      "import time\n",
      "start_time = time.time()\n",
      "for t in xrange(1,100): # the upper limit of the range should be ~1/2 of that of tmax!\n",
      "    # first term in the equation\n",
      "    temp = 0\n",
      "    for tprime in xrange(tmax-t):\n",
      "        temp += magnetization[tprime]*magnetization[tprime+t]\n",
      "    temp = (1./(tmax-t))*temp\n",
      "    # second term in the equation\n",
      "    temp1 = 0\n",
      "    for tprime in xrange(tmax-t):\n",
      "        temp1 += magnetization[tprime]\n",
      "    temp2 = 0\n",
      "    for tprime in xrange(tmax-t):\n",
      "        temp2 += magnetization[tprime+t]\n",
      "    tempo = (1./((tmax-t)**2))*temp1*temp2\n",
      "    # auto-correlation function value\n",
      "    chi.append(temp-tempo)\n",
      "plt.hold(True)\n",
      "plt.plot(np.asarray(chi)-110,label='old method')\n",
      "print time.time()-start_time\n",
      "# second way by summing elements using numpy.sum and some array manipulation\n",
      "chi = []\n",
      "start_time = time.time()\n",
      "for t in xrange(1,100): # the upper limit of the range should be ~1/2 of that of tmax!\n",
      "    # first term in the equation\n",
      "    #temp = 0\n",
      "    temp_array_1 = np.asarray(magnetization[0:tmax-t])\n",
      "    temp_array_2 = np.asarray(magnetization[t-1:tmax-1])\n",
      "    temp = (1./(tmax-t))*np.sum(temp_array_1*temp_array_2)\n",
      "    # second term in the equation\n",
      "    #temp1 = 0\n",
      "    temp_array = np.asarray(magnetization[0:tmax-t])\n",
      "    temp = (1./(tmax-t))*np.sum(temp_array)\n",
      "    #temp2 = 0\n",
      "    temp_array = np.asarray(magnetization[t-1:tmax-1])\n",
      "    temp2 = (1./(tmax-t))*np.sum(temp_array)\n",
      "    tempo = temp1*temp2\n",
      "    # auto-correlation function value\n",
      "    chi.append(temp-tempo)\n",
      "print time.time()-start_time\n",
      "plt.plot(chi,label='new method')\n",
      "plt.legend(loc='upper right')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1-d ising model properties with increasing system size\n",
      "======"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#lattice = np.ones(200) # initializing the lattice with all ones\n",
      "#lattice = np.zeros(200) # initializing the lattice randomly\n",
      "#for i in xrange(200):\n",
      "#    temp = np.random.random()\n",
      "#    if temp > 1./2:\n",
      "#        lattice[i] = 1\n",
      "#    else :\n",
      "#        lattice[i] = -1\n",
      "\n",
      "def initialize(i):\n",
      "    lattice = np.zeros(i)\n",
      "    for i in xrange(i):\n",
      "        temp = np.random.random()\n",
      "        if temp > 1./2:\n",
      "            lattice[i] = 1\n",
      "        else :\n",
      "            lattice[i] = -1\n",
      "    return lattice\n",
      "        \n",
      "# defines the local energy i.e product of neighbor spins.\n",
      "# used to compare the change in energy before and after a flip\n",
      "# with the boundary condition that the 0th spin is coupled to the nth spin\n",
      "def energy_local(site):\n",
      "    if site == 0:\n",
      "        return lattice[0]*lattice[1] - lattice[0]*lattice[-1]\n",
      "    elif site == len(lattice)-1 :\n",
      "        return lattice[len(lattice)-1]*lattice[len(lattice)-2] - lattice[len(lattice)-1]*lattice[0]\n",
      "    else :\n",
      "        return lattice[site]*lattice[site-1] - lattice[site]*lattice[site+1]\n",
      "    \n",
      "#def energy_local(site):\n",
      "#    if site == len(lattice)-1:\n",
      "#        return lattice[i]*lattice[i-1] + lattice[i]*lattice[0]\n",
      "#    else :\n",
      "#        return lattice[i]*lattice[i-1] + lattice[i]*lattice[i+1]\n",
      "\n",
      "# computes the total energy of the system i.e sum of products of all spins\n",
      "# assuming J = 1\n",
      "def global_energy():\n",
      "    temp = 0\n",
      "    for i in xrange(len(lattice)-1):\n",
      "        temp += -(lattice[i-1]*lattice[i]+lattice[i]*lattice[i+1])\n",
      "    return (1./2)*temp/len(lattice)\n",
      "\n",
      "# computing the total magnetization i.e the sum of all spins in the lattice\n",
      "def global_magnetization():\n",
      "    return np.sum(lattice)/len(lattice)\n",
      "\n",
      "#T = np.array([5,5./2,1,1./2,2./10])\n",
      "#betaJ = 1./T\n",
      "#T = 1./2\n",
      "T = 2./10\n",
      "bJ = 1./T\n",
      "for i in [10,50,100,200]:\n",
      "#for bJ in betaJ:\n",
      "    plt.hold(True)\n",
      "    plt.legend(loc='upper center')\n",
      "    lattice = initialize(i)\n",
      "    print lattice\n",
      "    global_e = []\n",
      "    global_e.append(global_energy())                             # the initial system energy\n",
      "    magnetization = []\n",
      "    magnetization.append(global_magnetization())                 # the initial system magnetization\n",
      "    accepted_moves = 0\n",
      "    for step in xrange(1000):\n",
      "        for mcsweep in xrange(i):                              \n",
      "            site = np.random.choice(np.arange(i))      # choose a site randomly from the lattice\n",
      "            pre_flip_e = energy_local(site)                      # compute local energy before flip\n",
      "            lattice[site] = -lattice[site]  \n",
      "            post_flip_e = energy_local(site)                     # compute local energy after flip\n",
      "            if post_flip_e - pre_flip_e < 0:\n",
      "    #            global_e.append(global_energy())                # update the system energy at this step\n",
      "                accepted_moves += 1\n",
      "    #            magnetization.append(global_magnetization())    # update the system magnetization at this step\n",
      "            else :\n",
      "                temp = np.random.random()\n",
      "                if temp < np.exp(-bJ*(post_flip_e - pre_flip_e)):\n",
      "    #                global_e.append(global_energy())\n",
      "                    accepted_moves += 1\n",
      "    #                magnetization.append(global_magnetization())\n",
      "                else :\n",
      "                    lattice[site] = -lattice[site]               # reverse the flip to initial state if the transition isnt valid\n",
      "    #                global_e.append(global_energy())\n",
      "    #                magnetization.append(global_magnetization())\n",
      "        global_e.append(global_energy())\n",
      "        magnetization.append(global_magnetization())\n",
      "    print \"accepted_moves\", accepted_moves, \"temperature\", i\n",
      "    print i, np.mean(global_e), np.mean(magnetization), np.var(global_e), np.var(magnetization)\n",
      "    plt.subplot(121)\n",
      "    plt.plot(global_e,label=i)\n",
      "    plt.subplot(122)\n",
      "    plt.plot(magnetization,label=i)\n",
      "    # to measure the auto-correlation of magnetization or correlation time!\n",
      "    #tmax = len(magnetization) # the total number of iterations\n",
      "    #chi = []\n",
      "    #for t in xrange(1,i/10): # the upper limit of the range should be ~1/2 of that of tmax!\n",
      "        # first term in the equation\n",
      "    #    temp = 0\n",
      "    #    for tprime in xrange(tmax-t):\n",
      "    #        temp += magnetization[tprime]*magnetization[tprime+t]\n",
      "    #    temp = (1./(tmax-t))*temp\n",
      "        # second term in the equation\n",
      "    #    temp1 = 0\n",
      "    #    for tprime in xrange(tmax-t):\n",
      "    #        temp1 += magnetization[tprime]\n",
      "    #    temp2 = 0\n",
      "    #    for tprime in xrange(tmax-t):\n",
      "    #        temp2 += magnetization[tprime+t]\n",
      "    #    tempo = (1./((tmax-t)**2))*temp1*temp2\n",
      "    #    chi.append(temp-tempo)\n",
      "    #plt.subplot(133)\n",
      "    #plt.plot(chi,label=i)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-1.  1. -1.  1.  1.  1. -1.  1. -1. -1.]\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 7016 temperature 10\n",
        "10 0.0284715284715 0.0203796203796 0.0806179434951 0.0971670886556\n",
        "[ 1. -1. -1. -1.  1.  1. -1. -1. -1.  1. -1.  1. -1.  1. -1. -1.  1. -1.\n",
        "  1. -1.  1. -1.  1. -1.  1.  1.  1.  1.  1. -1.  1.  1.  1. -1.  1. -1.\n",
        "  1. -1.  1. -1. -1. -1.  1. -1.  1.  1.  1. -1.  1. -1.]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 37160 temperature 50\n",
        "50 0.0031968031968 0.0101498501499 0.0194726975322 0.0192887887337\n",
        "[ 1.  1.  1.  1.  1. -1.  1. -1. -1.  1. -1. -1. -1. -1. -1.  1. -1.  1.\n",
        " -1.  1. -1.  1. -1. -1.  1.  1. -1. -1.  1. -1.  1. -1.  1. -1.  1. -1.\n",
        "  1. -1.  1. -1. -1. -1. -1. -1. -1.  1. -1. -1.  1.  1. -1.  1. -1. -1.\n",
        " -1.  1.  1.  1. -1. -1. -1. -1.  1.  1. -1. -1.  1. -1. -1. -1. -1.  1.\n",
        " -1.  1. -1. -1. -1.  1.  1. -1. -1. -1.  1.  1. -1. -1. -1.  1.  1.  1.\n",
        "  1. -1.  1. -1.  1.  1.  1. -1. -1. -1.]\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74420 temperature 100\n",
        "100 0.00145854145854 0.00173826173826 0.0102719985309 0.0102503250995\n",
        "[-1. -1.  1. -1. -1. -1.  1.  1.  1. -1.  1.  1.  1.  1. -1. -1.  1. -1.\n",
        " -1.  1. -1.  1.  1.  1.  1.  1.  1. -1. -1.  1.  1. -1. -1.  1. -1. -1.\n",
        "  1.  1.  1.  1. -1. -1. -1. -1.  1.  1.  1.  1.  1.  1. -1.  1. -1.  1.\n",
        "  1. -1.  1. -1.  1.  1. -1. -1.  1. -1. -1. -1. -1.  1.  1. -1. -1. -1.\n",
        "  1. -1. -1.  1. -1. -1. -1.  1.  1. -1.  1.  1. -1. -1. -1.  1. -1.  1.\n",
        " -1. -1. -1.  1. -1.  1. -1. -1.  1. -1. -1.  1.  1.  1.  1.  1. -1.  1.\n",
        "  1.  1.  1.  1.  1.  1.  1. -1.  1. -1. -1.  1.  1.  1. -1. -1.  1.  1.\n",
        " -1. -1. -1.  1. -1.  1. -1.  1. -1. -1.  1. -1. -1.  1. -1.  1.  1.  1.\n",
        " -1. -1.  1. -1.  1. -1.  1.  1.  1.  1.  1. -1. -1.  1. -1.  1. -1. -1.\n",
        "  1. -1. -1. -1.  1.  1.  1.  1.  1.  1. -1. -1. -1. -1.  1. -1. -1.  1.\n",
        "  1. -1. -1.  1. -1.  1. -1. -1.  1. -1.  1.  1. -1.  1.  1. -1.  1.  1.\n",
        " -1. -1.]\n",
        "accepted_moves"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 149608 temperature 200\n",
        "200 -0.00156343656344 0.0035964035964 0.00516201620557 0.00491593701004\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GljRVq1YlJSUFgD59+lBUVMRel526RMWy6NAhi+7duwPmNg36dgxuiNRFy4kJhHvH7b68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\nwJQBg8FgMMCUAYPBYDAA/D8ofPDPoX5jCQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb155ccec>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "work in-progress\n",
      "======="
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#for i in xrange(len(lattice)-1):\n",
      "    #print lattice[i]*lattice[i-1] + lattice[i]*lattice[i+1]\n",
      "def energy_temp(site):\n",
      "    if site == len(lattice)-1:\n",
      "        return lattice[i]*lattice[i-1] + lattice[i]*lattice[0]\n",
      "    else :\n",
      "        return lattice[i]*lattice[i-1] + lattice[i]*lattice[i+1]\n",
      "for i in xrange(len(lattice)-1):\n",
      "    print i, energy_temp(i)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0 2.0\n",
        "1 2.0\n",
        "2 0.0\n",
        "3 0.0\n",
        "4 0.0\n",
        "5 -2.0\n",
        "6 -2.0\n",
        "7 -2.0\n",
        "8 -2.0\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}