ProppWilsonAlgorithm_for_IsingModel _MCM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Propp Wilson Algorithm for the Ferromagnetic Ising Model #"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Ferromagnetism</b> arises when a collection of atomic spins align such that their associated magnetic moments all point in the same direction, yielding a net magnetic moment which is macroscopic in the size. The simplest  theoretical description of ferromagnetism is called the <b>Ising Model</b>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I implemented the <b>2D Ferromagnetic Ising Model</b> using Propp Wilson Algorithms in this project."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Functions of the Ising Model:</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* `runIsing(t, state, U):`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* `updateState(t, state, U):`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* `calcEnergyDiff(i, j, state):`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* `InitialState(N):`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Declaration of the libraries used in the program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
      "\u001b[32m\u001b[1m  Updating\u001b[22m\u001b[39m git-repo `https://github.com/JuliaRegistries/General.git`\n",
      "\u001b[?25l\u001b[2K\u001b[?25h"
     ]
    }
   ],
   "source": [
    "using Pkg; Pkg.activate(\".\"); Pkg.instantiate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Distributions, LinearAlgebra\n",
    "using Plots; pyplot(); default(legendfontsize = 15.0, linewidth = 2.0)\n",
    "using Random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": true
   },
   "source": [
    "### Utility Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InitialState (generic function with 1 method)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function InitialState(N)  # Generates an initial state with all values fixed to +1 and -1\n",
    "    state = zeros(3, N, N)\n",
    "    for i in 1:N\n",
    "        for j in 1:N\n",
    "            state[1, i, j] = 1\n",
    "            state[2, i, j] = -1\n",
    "        end\n",
    "    end\n",
    "    return state\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Calculate the energy difference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"is-2.jpg\" width=\"400\" height=\"200\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "calcEnergyDiff (generic function with 1 method)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function calcEnergyDiff(i, j, state)  # Calculate the energy at flipping the vertex at [i,j]\n",
    "    m = size(state, 2)\n",
    "    if i == 1\n",
    "        top = 1\n",
    "    else\n",
    "        top = state[i - 1, j]\n",
    "    end\n",
    "    if i == m\n",
    "        bottom = 1\n",
    "    else\n",
    "        bottom = state[i + 1, j]\n",
    "    end\n",
    "    if j == 1\n",
    "        left = 1\n",
    "    else\n",
    "        left = state[i, j - 1]\n",
    "    end\n",
    "            \n",
    "    if j == m\n",
    "        right = 1\n",
    "    else\n",
    "        right = state[i, j + 1]\n",
    "    end\n",
    "\n",
    "    energy = 2 * state[i, j] * sum([top, bottom, left, right])  # Energy calculated by given formula\n",
    "                \n",
    "    return energy\n",
    "end\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Update State for Ising Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "k = Boltzmann constant. We assume that k equals to 1.\n",
    "<a href=\"https://www.codecogs.com/eqnedit.php?latex=\\beta&space;=1/kT\" target=\"_blank\"><img src=\"https://latex.codecogs.com/gif.latex?\\beta&space;=1/kT\" title=\"\\beta =1/kT\" /></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The probability measure:\n",
    "\n",
    "<img src=\"is-1.jpg\" width=\"400\" height=\"200\">\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "updateState (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function updateState(t, state, U,T)\n",
    "    B = 1 / T\n",
    "    E = zeros(3)# Initialize Energy\n",
    "\n",
    "    i = Int(U[2,Int(-t)])  # Picks a random vertex, the same each time the chain runs from 1\n",
    "    j = Int(U[3,Int(-t)])\n",
    "    \n",
    "    for h in 1:3\n",
    "\n",
    "        E[h] =  calcEnergyDiff(i, j, state[h,:,:])  # Find energy under randomly generated flip of each state space separately\n",
    "\n",
    "        u = U[1,Int(-t)]\n",
    "        if state[h, i, j] == 1\n",
    "            u = 1 - u\n",
    "        end\n",
    "        \n",
    "        if u < 0.5 * (1 - tanh(0.5 * B * E[h]))  # condition to accept change, random number is the same each time\n",
    "            state[h, i, j] = -state[h, i, j]\n",
    "            #n[h]=1\n",
    "        else\n",
    "            state[h, i, j] = state[h, i, j]\n",
    "            #n[h]=0\n",
    "        end\n",
    "    end\n",
    "    return state  # returns both states\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ising Model Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "runIsing (generic function with 1 method)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function runIsing(t, state, U, T)  # Runs chain from the designated starting time until time 0\n",
    "\n",
    "    while t < 0\n",
    "        state = updateState(t, state, U,T)\n",
    "        t += 1\n",
    "    end\n",
    "    return state\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propp Wilson Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Introduction to Propp Wilson Algorithm</b>\n",
    "\n",
    "The propp-Wilson Algorithm solves two different problems\n",
    "* s' is distributed exactly π (\" perfect simulation \")\n",
    "* The algorithm <b>stops</b> automatically"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pseudocode of the algorithm:\n",
    "\n",
    "<b>1. </b> Set 𝑚 = 1\n",
    "\n",
    "<b>2. </b> For each 𝑠 ∈ 𝑆, simulate the Markov chain starting at time −𝑁𝑚 in state 𝑠 \n",
    "\n",
    "and running up to time 0 using the update function 𝜙 with the sequence 𝑈−𝑁𝑚 +1,𝑈−𝑁𝑚 +2, … ,𝑈−1,𝑈0\n",
    "\n",
    "<b>3. </b> If all 𝑘 chains end up in the same state s at time 0, output s and stop\n",
    "\n",
    "<b>4. </b> Set 𝑚: = 𝑚 + 1 and go to step 2\n",
    "\n",
    "<b>Note:</b> The same sequence 𝑈0,𝑈−1, … is used for all 𝑘 chains.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Functions in Propp Wilson Algorithm</b>\n",
    "* 1. runProppWilson(N,j):\n",
    "* 2. genRandomness(N,M): \n",
    "* 3. genStartingTimes(j):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "``genRandomness(N,M)``: generates a sequence of i.i.d. random numbers for Propp-Wilson Algorithm\n",
    "````\n",
    "\n",
    "U0,U1,U2...\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "genRandomness (generic function with 1 method)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function genRandomness(N, M)  # generate and store three sets of random numbers\n",
    "    U = zeros(3, M)\n",
    "\n",
    "    U[2,:] = rand(1:N, M) # Random numbners i\n",
    "    U[3,:] = rand(1:N, M)  # Random numbners j\n",
    "    for i in 1:M\n",
    "        U[1,i] = rand()  # Random numbners U\n",
    "    end\n",
    "    return U\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "``genStartingTimes(j)``: to generate the starting times, the function generates the sequence of the positive numbers like (N1,N2...) = (1,2,4,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "genStartingTimes (generic function with 1 method)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function genStartingTimes(j)  # Creates starting times, each one is double the previous\n",
    "    M = zeros(j)\n",
    "    M[2] = 1\n",
    "    for x in 3:j\n",
    "        M[x] = 2 * M[x - 1]\n",
    "    end       \n",
    "    return M\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "* Propp Wilson Algorithm call the Ising model to run chain from the designated starting time until time 0 after each magnetization\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Magnetization Formula</b> :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "runProppWilson (generic function with 1 method)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function runProppWilson(N,j,T)\n",
    "    M = genStartingTimes(j)# negative integers (-1,-2,-4,-8)\n",
    "    U = genRandomness(N, 1)# U1,U2,U3...\n",
    "    state = InitialState(N)\n",
    "    m=2\n",
    "    before = InitialState(N)\n",
    "    while state[1,:,:] != state[2,:,:]  # Condition for termination: both state spaces are the same\n",
    "        \n",
    "        U = hcat(U,genRandomness(N, Int(M[m] - M[m-1]))) # Generates more random numbers when necessary\n",
    "        \n",
    "        magnetization = sum([sum(i) for i in state[1,:,:]])-sum([sum(i) for i in state[2,:,:]])\n",
    "        \n",
    "        println(\"magnetization= \",magnetization, \"round= \", m-1)\n",
    "        state = runIsing(-Int(M[m]), state,U, T)\n",
    "        m += 1  # If states are not the same, goes to the next starting time\n",
    "        if state[1,:,:] != state[2,:,:]\n",
    "            before[2,:,:] = state[2,:,:]\n",
    "        end\n",
    "    end\n",
    "    return state[1,:,:], before[2,:,:]\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph ##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Main Program  and Visualisation of the Result\n",
    "* This Graph function below call the ProppWilson Algorithm.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Python code for simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Pkg.build(\"PyCall\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyCall"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "py\"\"\"\n",
    "import random\n",
    "import numpy as np\n",
    "from numpy.random import rand\n",
    "import matplotlib\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "def Graph(state, T):\n",
    "    S = state.shape[1]  # Takes the size of the matrix\n",
    "    print(\"Plotting!\")\n",
    "    for i in range(S):\n",
    "        for j in range(S):\n",
    "            if state[i][j] == 1:  # Graphs a red + if the matrix entry is positive\n",
    "                plt.scatter(j, S - 1 - i, c='r', marker=',', )#s=(150,))\n",
    "            elif state[i][j] == -1:  # Graphs a blue minus is the matrix is negative\n",
    "                plt.scatter(j, S - 1 - i, c='b', marker=',', )#s=(150,))\n",
    "    plt.title(\"Sample, T=%d\" % (T) )\n",
    "    print(\"Done!\")\n",
    "    plt.show()\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Graph (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function Graph(N, j, T)\n",
    "    state, = runProppWilson(N, j,T)\n",
    "    py\"Graph\"(state,T)\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 200.0round= 1\n",
      "magnetization= 200.0round= 2\n",
      "magnetization= 200.0round= 3\n",
      "magnetization= 198.0round= 4\n",
      "magnetization= 196.0round= 5\n",
      "magnetization= 194.0round= 6\n",
      "magnetization= 192.0round= 7\n",
      "magnetization= 184.0round= 8\n",
      "magnetization= 164.0round= 9\n",
      "magnetization= 144.0round= 10\n",
      "magnetization= 112.0round= 11\n",
      "magnetization= 70.0round= 12\n",
      "magnetization= 6.0round= 13\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0; … ; 1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0], [1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0; … ; 1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state, before = runProppWilson(10,20,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Last State of Magnetization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "py\"Graph\"(state,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The State of Ising Model before the laste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAABnKBYAAMAZigUAAHCGYgEAAJyhWAAAAGcoFgAAwBmKBQAAcIZiAQAAnKFYAAAAZygWAADAGYoFAABwhmIBAACcoVgAAABnKBYAAMAZigUAAHCGYgEAAJyhWAAAAGcoFgAAwBmKBQAAcIZiAQAAnKFYAAAAZ5L9HsCZaFQqL6//+XBYyslpuXmaykIOAxkMRKhmIYiFDJKNHBYySDZyBDhDwsXis88+0+zZs/XSSy/pu+++U25urlauXKlBgwY1x3yNE41KubkNr1dSEuxfFgs5DGQwEKGahSAWMkg2cljIINnIEfAMCRWLr7/+WsOGDdPo0aP10ksvqWvXrvrkk0902mmnNdd8jXOi1taU9fxiIYeBDAYiVLMQxEIGyUYOCxkkGzkCniGhYrFo0SJlZmZq1apVNct69erleiYAAHCKSujDm+vXr9fgwYN1zTXXqGvXrhowYIBWrFhxwm0qKioUj8drPQAAgE0JFYu9e/dq2bJlysnJ0SuvvKJbb71Vt99+u/785z/Xu01BQYEikUjNIzMz86SHBgAAwZRQsaiqqtLAgQO1cOFCDRgwQLfccotuvvlmLVu2rN5t8vPzFYvFah6lpaUnPTQAAAimhIpFRkaGzjvvvFrL+vTpo/3799e7TUpKitLT02s9AACATQkVi2HDhunjjz+utaykpERZWVlOhwIAAKemhIrFHXfcoa1bt2rhwoX65z//qTVr1qiwsFB5eXnNNV/jhMNu1/OLhRwGMhiIUM1CEAsZJBs5LGSQbOQIeIaQ53leIhu88MILys/PVzQaVXZ2tmbNmqWbb7650dvH43FFIhHFYjG3l0UCfBeyhFjIYSCDgQjVLASxkEGykcNCBslGDh8yNPb4nXCxOFnNViwAAECzaezxmy8hAwAAzlAsAACAMxQLAADgDMUCAAA4Q7EAAADOUCwAAIAzFAsAAOAMxQIAADhDsQAAAM5QLAAAgDMUCwAA4AzFAgAAOEOxAAAAzlAsAACAMxQLAADgDMUCAAA4Q7EAAADOUCwAAIAzFAsAAOAMxQIAADhDsQAAAM5QLAAAgDMUCwAA4AzFAgAAOEOxAAAAziT7PYAz0ahUXl7/8+GwlJPTcvM0lYUcZAgOAzkMRKhmIYiFDJKNHAHOYKNYRKNSbm7D65WUBPuXxUIOMgSHgRwGIlSzEMRCBslGjoBnsHEp5EStrSnr+cVCDjIEh4EcBiJUsxDEQgbJRo6AZ7BRLAAAQCBQLAAAgDMUCwAA4AzFAgAAOEOxAAAAzlAsAACAMzaKRTjsdj2/WMhBhuAwkMNAhGoWgljIINnIEfAMIc/zvJbcYTweVyQSUSwWU3p6ursXDvBdyBJiIQcZgsNADgMRqlkIYiGDZCOHDxkae/y2UywAAECzaezx28alEAAAEAgUCwAA4AzFAgAAOEOxAAAAzlAsAACAMxQLAADgDMUCAAA4Q7EAAADOUCwAAIAzFAsAAOAMxQIAADhDsQAAAM5QLAAAgDMUCwAA4AzFAgAAOEOxAAAAzlAsAACAMxQLAADgDMUCAAA4Q7EAAADOUCwAAIAzFAsAAOAMxQIAADhDsQAAAM5QLAAAgDPJfg/gTDQqlZfX/3w4LOXktNw8TWUhBxmCw0IOCxkkGzksZJBs5AhyBu8kLFy40JPkzZgxo9HbxGIxT5IXi8VOZte1lZR4ntTwo6TE3T6bg4UcZAgOCzksZPA8GzksZPA8Gzl8ytDY43eTL4Vs27ZNhYWFOv/8852VnCY7UWtrynp+sZCDDMFhIYeFDJKNHBYySDZyBDxDk4rF4cOHdf3112vFihU6/fTTXc8EAABOUU0qFnl5eRo/frzGjBnT4LoVFRWKx+O1HgAAwKaEP7z5zDPPaOfOndq2bVuj1i8oKND999+f8GAAAODUk9AZi9LSUs2YMUNPPvmk2rdv36ht8vPzFYvFah6lpaVNGhQAAARfQmcsduzYobKyMg0aNKhmWWVlpTZt2qRHH31UFRUVSkpKqrVNSkqKUlJS3EwLAAACLaFicfHFF+vdd9+ttWzq1Knq3bu3Zs+eXadUAACA1iWhYhEOh9WvX79ay9LS0tS5c+c6y1tUOOx2Pb9YyEGG4LCQw0IGyUYOCxkkGzkCnsHGnTdzcqSSkuDehayxLOQgQ3BYyGEhg2Qjh4UMko0cAc8Q8jzPa8kdxuNxRSIRxWIxpaent+SuAQBAEzX2+M2XkAEAAGcoFgAAwBmKBQAAcIZiAQAAnKFYAAAAZygWAADAGYoFAABwhmIBAACcoVgAAABnKBYAAMAZigUAAHCGYgEAAJyhWAAAAGcoFgAAwBmKBQAAcIZiAQAAnKFYAAAAZygWAADAGYoFAABwhmIBAACcoVgAAABnKBYAAMAZigUAAHCGYgEAAJyhWAAAAGeS/R7AmWhUKi+v//lwWMrJabl5mspCDjIEh4UcFjJINnJYyCDZyBHgDDaKRTQq5eY2vF5JSbB/WSzkIENwWMhhIYNkI4eFDJKNHAHPYONSyIlaW1PW84uFHGQIDgs5LGSQbOSwkEGykSPgGWwUCwAAEAgUCwAA4AzFAgAAOEOxAAAAzlAsAACAMxQLAADgjI1iEQ67Xc8vFnKQITgs5LCQQbKRw0IGyUaOgGcIeZ7nteQO4/G4IpGIYrGY0tPT3b1wgO9ClhALOcgQHBZyWMgg2chhIYNkI4cPGRp7/LZTLAAAQLNp7PHbxqUQAAAQCBQLAADgDMUCAAA4Q7EAAADOUCwAAIAzFAsAAOAMxQIAADhDsQAAAM5QLAAAgDMUCwAA4AzFAgAAOEOxAAAAzlAsAACAMxQLAADgDMUCAAA4Q7EAAADOUCwAAIAzFAsAAOAMxQIAADhDsQAAAM5QLAAAgDMUCwAA4AzFAgAAOEOxAAAAzlAsAACAM8l+D+BMNCqVl9f/fDgs5eS03DxNZSEHGYLDQg4LGSQbOSxkkGzkCHCGhIpFQUGBnnvuOX300UdKTU3V0KFDtWjRIp177rnNNV/jRKNSbm7D65WUBPuXxUIOMgSHhRwWMkg2cljIINnIEfAMCV0K2bhxo/Ly8rR161YVFRXp6NGjGjt2rL755pvmmq9xTtTamrKeXyzkIENwWMhhIYNkI4eFDJKNHAHPkNAZi5dffrnWz6tWrVLXrl21Y8cOjRgxwulgAADg1HNSn7GIxWKSpE6dOtW7TkVFhSoqKmp+jsfjJ7NLAAAQYE3+qxDP8zRr1iwNHz5c/fr1q3e9goICRSKRmkdmZmZTdwkAAAKuycVi+vTpeuedd/T000+fcL38/HzFYrGaR2lpaVN3CQAAAq5Jl0Juu+02rV+/Xps2bVKPHj1OuG5KSopSUlKaNBwAADi1JFQsPM/Tbbfdpueff17FxcXKzs5urrkAAMApKKFikZeXpzVr1mjdunUKh8M6dOiQJCkSiSg1NbVZBmyUcNjten6xkIMMwWEhh4UMko0cFjJINnIEPEPI8zyv0SuHQsddvmrVKk2ZMqVRrxGPxxWJRBSLxZSent7YXTcswHchS4iFHGQIDgs5LGSQbOSwkEGykcOHDI09fidULFxotmIBAACaTWOP33wJGQAAcIZiAQAAnKFYAAAAZygWAADAGYoFAABwhmIBAACcoVgAAABnKBYAAMAZigUAAHCGYgEAAJyhWAAAAGcoFgAAwBmKBQAAcIZiAQAAnKFYAAAAZygWAADAGYoFAABwhmIBAACcoVgAAABnKBYAAMAZigUAAHCGYgEAAJyhWAAAAGcoFgAAwBmKBQAAcCbZ7wGciUal8vL6nw+HpZyclpunqSzkIENwWMhhIYNkIoeBCNUsBAlwBhvFIhqVcnMbXq+kJNi/LBZykCE4LOSwkEEykcNAhGoWggQ8g41LISdqbU1Zzy8WcpAhOCzksJBBMpHDQIRqFoIEPIONYgEAAAKBYgEAAJyhWAAAAGcoFgAAwBmKBQAAcIZiAQAAnLFRLMJht+v5xUIOMgSHhRwWMkgmchiIUM1CkIBnCHme57XkDuPxuCKRiGKxmNLT0929cIDvQpYQCznIEBwWcljIIJnIYSBCNQtBfMjQ2OO3nWIBAACaTWOP3zYuhQAAgECgWAAAAGcoFgAAwBmKBQAAcIZiAQAAnKFYAAAAZygWAADAGYoFAABwhmIBAACcoVgAAABnKBYAAMAZigUAAHCGYgEAAJyhWAAAAGcoFgAAwBmKBQAAcIZiAQAAnKFYAAAAZygWAADAGYoFAABwhmIBAACcoVgAAABnKBYAAMAZigUAAHAm2e8BnIlGpfLy+p8Ph6WcnJabp6ks5CBDcFjIYSGDZCOHhQySjRwBzmCjWESjUm5uw+uVlAT7l8VCDjIEh4UcFjJINnJYyCDZyBHwDE26FLJ06VJlZ2erffv2GjRokDZv3ux6rsScqLU1ZT2/WMhBhuCwkMNCBslGDgsZJBs5Ap4h4WKxdu1azZw5U3PnztWuXbt00UUX6dJLL9X+/fubYz4AAHAKSbhYPPzww7rxxht10003qU+fPnrkkUeUmZmpZcuWHXf9iooKxePxWg8AAGBTQsXi+++/144dOzR27Nhay8eOHas33njjuNsUFBQoEonUPDIzM5s+LQAACLSEisWXX36pyspKdevWrdbybt266dChQ8fdJj8/X7FYrOZRWlra9GkBAECgNemvQkKhUK2fPc+rs+yYlJQUpaSkNGU3AADgFJPQGYsuXbooKSmpztmJsrKyOmcxAABA65NQsWjXrp0GDRqkoqKiWsuLioo0dOhQp4MlJBx2u55fLOQgQ3BYyGEhg2Qjh4UMko0cAc8Q8jzPS2SDtWvX6oYbbtBjjz2mIUOGqLCwUCtWrND777+vrKysBrePx+OKRCKKxWJKT09v8uB1BPguZAmxkIMMwWEhh4UMko0cFjJINnL4kKGxx++Ei4VUfYOsxYsX6+DBg+rXr5+WLFmiESNGOB0MAAAER7MWi5NBsQAA4NTT2OM3324KAACcoVgAAABnKBYAAMAZigUAAHCGYgEAAJyhWAAAAGcoFgAAwBmKBQAAcIZiAQAAnKFYAAAAZygWAADAmeSW3uGxryaJx+MtvWsAANBEx47bDX3FWIsXi/L/9zWvmZmZLb1rAABwksrLyxWJROp9vsW/3bSqqkoHDhxQOBxWKBRqln3E43FlZmaqtLSUb1D1Ge9FcPBeBAfvRXDwXjSe53kqLy9X9+7d1aZN/Z+kaPEzFm3atFGPHj1aZF/p6en8ogQE70Vw8F4EB+9FcPBeNM6JzlQcw4c3AQCAMxQLAADgTNL8+fPn+z1Ec0hKStKoUaOUnNziV3vwX3gvgoP3Ijh4L4KD98KtFv/wJgAAsItLIQAAwBmKBQAAcIZiAQAAnKFYAAAAZygWAADAGZPFYunSpcrOzlb79u01aNAgbd682e+RWp2CggL96Ec/UjgcVteuXXXFFVfo448/9nusVq+goEChUEgzZ870e5RW6bPPPtOkSZPUuXNndejQQRdccIF27Njh91itztGjRzVv3jxlZ2crNTVVZ511lv7nf/5HVVVVfo9mgrlisXbtWs2cOVNz587Vrl27dNFFF+nSSy/V/v37/R6tVdm4caPy8vK0detWFRUV6ejRoxo7dqy++eYbv0drtbZt26bCwkKdf/75fo/SKn399dcaNmyY2rZtq5deekkffPCBHnroIZ122ml+j9bqLFq0SI899pgeffRRffjhh1q8eLF++9vf6g9/+IPfo5lg7j4WP/nJTzRw4EAtW7asZlmfPn10xRVXqKCgwMfJWrcvvvhCXbt21caNGzVixAi/x2l1Dh8+rIEDB2rp0qV64IEHdMEFF+iRRx7xe6xWZc6cOXr99dc5gxoAl112mbp166aVK1fWLLv66qvVoUMHPfHEEz5OZoOpMxbff/+9duzYobFjx9ZaPnbsWL3xxhs+TQVJisVikqROnTr5PEnrlJeXp/Hjx2vMmDF+j9JqrV+/XoMHD9Y111yjrl27asCAAVqxYoXfY7VKw4cP14YNG1RSUiJJ2rNnj7Zs2aJx48b5PJkNpu5f+uWXX6qyslLdunWrtbxbt246dOiQT1PB8zzNmjVLw4cPV79+/fwep9V55plntHPnTm3btoZ8+f8AAALhSURBVM3vUVq1vXv3atmyZZo1a5buuecevf3227r99tuVkpKiX/ziF36P16rMnj1bsVhMvXv3VlJSkiorK7VgwQJdd911fo9mgqlicUwoFKr1s+d5dZah5UyfPl3vvPOOtmzZ4vcorU5paalmzJihf/zjH2rfvr3f47RqVVVVGjx4sBYuXChJGjBggN5//30tW7aMYtHC1q5dqyeffFJr1qxR3759tXv3bs2cOVPdu3fX5MmT/R7vlGeqWHTp0kVJSUl1zk6UlZXVOYuBlnHbbbdp/fr12rRpk3r06OH3OK3Ojh07VFZWpkGDBtUsq6ys1KZNm/Too4+qoqJCSUlJPk7YemRkZOi8886rtaxPnz569tlnfZqo9brrrrs0Z84cTZw4UZLUv39/7du3TwUFBRQLB0x9xqJdu3YaNGiQioqKai0vKirS0KFDfZqqdfI8T9OnT9dzzz2nV199VdnZ2X6P1CpdfPHFevfdd7V79+6ax+DBg3X99ddr9+7dlIoWNGzYsDp/cl1SUqKsrCyfJmq9vv32W7VpU/vwl5SUxJ+bOmLqjIUkzZo1SzfccIMGDx6sIUOGqLCwUPv379ett97q92itSl5entasWaN169YpHA7XnEWKRCJKTU31ebrWIxwO1/lcS1pamjp37sznXVrYHXfcoaFDh2rhwoW69tpr9fbbb6uwsFCFhYV+j9bqTJgwQQsWLFDPnj3Vt29f7dq1Sw8//LCmTZvm92g2eAb98Y9/9LKysrx27dp5AwcO9DZu3Oj3SK2OpOM+Vq1a5fdord7IkSO9GTNm+D1Gq/T3v//d69evn5eSkuL17t3bKyws9HukVikej3szZszwevbs6bVv394766yzvLlz53oVFRV+j2aCuftYAAAA/5j6jAUAAPAXxQIAADhDsQAAAM5QLAAAgDMUCwAA4AzFAgAAOEOxAAAAzlAsAACAMxQLAADgDMUCAAA4Q7EAAADO/C9ut/1twiJy2gAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "py\"Graph\"(before,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 800.0round= 1\n",
      "magnetization= 800.0round= 2\n",
      "magnetization= 800.0round= 3\n",
      "magnetization= 800.0round= 4\n",
      "magnetization= 800.0round= 5\n",
      "magnetization= 800.0round= 6\n",
      "magnetization= 800.0round= 7\n",
      "magnetization= 796.0round= 8\n",
      "magnetization= 792.0round= 9\n",
      "magnetization= 778.0round= 10\n",
      "magnetization= 752.0round= 11\n",
      "magnetization= 726.0round= 12\n",
      "magnetization= 680.0round= 13\n",
      "magnetization= 530.0round= 14\n",
      "magnetization= 404.0round= 15\n",
      "magnetization= 256.0round= 16\n",
      "magnetization= 234.0round= 17\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([-1.0 -1.0 … 1.0 1.0; 1.0 1.0 … -1.0 1.0; … ; 1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0], [-1.0 -1.0 … 1.0 1.0; 1.0 1.0 … -1.0 1.0; … ; 1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state, before = runProppWilson(20,30,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "py\"Graph\"(state,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "py\"Graph\"(before,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 5000.0round= 1\n",
      "magnetization= 5000.0round= 2\n",
      "magnetization= 5000.0round= 3\n",
      "magnetization= 5000.0round= 4\n",
      "magnetization= 5000.0round= 5\n",
      "magnetization= 4998.0round= 6\n",
      "magnetization= 4998.0round= 7\n",
      "magnetization= 4996.0round= 8\n",
      "magnetization= 4990.0round= 9\n",
      "magnetization= 4984.0round= 10\n",
      "magnetization= 4958.0round= 11\n",
      "magnetization= 4918.0round= 12\n",
      "magnetization= 4830.0round= 13\n",
      "magnetization= 4672.0round= 14\n",
      "magnetization= 4476.0round= 15\n",
      "magnetization= 4254.0round= 16\n",
      "magnetization= 4124.0round= 17\n",
      "magnetization= 3692.0round= 18\n",
      "magnetization= 3410.0round= 19\n",
      "magnetization= 3082.0round= 20\n",
      "magnetization= 2760.0round= 21\n",
      "magnetization= "
     ]
    },
    {
     "data": {
      "image/png": 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nE/tK1BYAAEQBwwcAAPBUdE44dUnYz+i2+7cdOy8k1W2CfIwQPm6kvFg0zRm3jrWTbeiHuaIzfLiUdgnzGd2kIkLKxDPsDeJkQTQnXF00LaQ9c+tYO2HkInYm9pW0S5p1d/tdgfEy4/v9LgHpEI/7XYHR3Ep5uZrgCmnPIp+oM7GvPr02Rmf4yMnxuwLjDcvL8rsEpENent8VIFn0LJxM7KtPr43RGT6I2toikhlSJsb7MDh6Fk4m9pWoLQAAiAKGDwAA4KnopF0A4AScxOeJj7vDycKcbgny4pVO4shBjxFHZ/hwKWobaibGwJA6+jooI+PzIe2Zk4U53WLk4pUO+uokjuxqjJioLQAgzCIftXUgzIuX/rHoDB+kXeyZeCY2Ukdfg4eehZOJfSXtAgAAooDhAwAAeIrhAwAAeCo6aRfABiubAunlVqw5zNHnsK+cfkx0hg+itvZCGu9zwsiVTd0S4b4GVkh7ZmSs2UsO+ur5MSJqC/jHyJVNASCkojN8ELW1Z2IMDKmjr8FDz8LJxL4StQUAAFHA8AEAADzF8AEAADwVnbQLMAhWNgUA76Q0fNTV1enuu+/WnXfeqQcffFCS1NPToyVLluiZZ57RoUOHNHPmTK1Zs0YlJSWuFHzSiNraC2m8z4lQRwAj3NfAomfhZGJfgxa1bWpq0mOPPaZJkyb1u76mpkYbNmxQfX29Nm/erIMHD2rOnDnq6+tLuVgAABB8JzV8HDx4UNdff71++tOfauTIkYnrDxw4oHXr1un+++/XrFmzdM455+ipp55SS0uLXnnlFdeKPilEbe2ZGAND6uhr8NCzcDKxr0GK2i5YsECXX365Zs2a1e/65uZm9fb2qrq6OnFdcXGxJk6cqC1btpzwvnp6ehSPx/tdAABAeCV9zkd9fb22b9+upqam427r6OhQdnZ2v3dDJKmgoEAdHR0nvL+6ujr96Ec/SrYMAAAQUEkNH21tbbrzzju1ceNGDRs2zPHvWZaljIyME962dOlSLVq0KPFzPB5XaWlpMmUBgePWInZOtil3uD8WxAPglaSGj+bmZnV2dmrKlCmJ6/r6+vTGG29o9erVevnll3XkyBHt37+/37sfnZ2dqqysPOF9xmIxxWKxkyw/CaRd7Jl4JnYIubWInVMbW15Vtc3+jFwQL8p4LIaTiX0NQtpl5syZamlp0Y4dOxKXqVOn6vrrr0/8d1ZWlhoaGhK/097erp07dw44fHimu9vf/QcB59t4wq1F7JzqjNsP9yyIZxgei+FkYl99em1M6p2P3NxcTZw4sd91OTk5OvXUUxPX33LLLVq8eLFOPfVUjRo1SkuWLFFFRcVxJ6d6LifH3/0HQV6e3xUgHehr8NCzcDKxrz69Nrr+DacrV65UZmamrrnmmsSXjK1fv15Dhw51e1fJIWprz8QYGFJXMcl+G5iFx2I4mdhXn14bUx4+Ghsb+/08bNgwrVq1SqtWrUr1rgEAQAixsBwAAPAUC8sh8IIWI43psKPt3Fjo7sttym3vK8wL4pn29+GsHiDcojN8ELW1Z2IMzIaT2KppMdJs9dpu42bNr7ZsVKuq7TcMIdP+PpzGrPe0PKIz0l8OvGbic2wQoraAaZzEVk2LkXpd8xh1unZfQWPa34fTmPUhDU9zJYC/ojN8kHaxZ+KZ2EjZJNoaPDwWw8nEvgZpYTkAAICTxfABAAA8xfABAAA8FZ20C0IppsOBi5EGseagMu1YO6nH67V/AD9EZ/ggamvPxBiYjQnabVSM1gnPaw5gX91i2t+H03r2tjzsQTXwnImPRaK2AABJOkWH/C4BSKvoDB9Ebe2ZGAND6uhr4IypKPS7BKSDiY9ForYAACAKGD4AAICnGD4AAICnGD4AAICnojN8ELW1Z2IMDKmjr8FDz8LJxL769NoYneEDAAAYITrDB1FbeybGwJA6+ho89CycTOwrUVsAABAFDB8AAMBTDB8AAMBT0VlYDkCgtGrcoCu85qpL5Xrfs/sB4J7oDB9Ebe2ZGAND6gLY11aN03i1DrrNOLXarhDr1v14LoA9gwMm9pVVbQHgS4O9U3FMrro8ux8A7orO8EHU1p6JMTCkjr4GDz0LJxP7StQWAABEAcMHAADwVHROOAUQGDEd1ji1Dno+RqnsTyJ3634AuCs6wwdpF3smnomN1AWwrxO025UEilv347kA9gwOmNhX0i5p1t3tdwXmi8f9rgDpQF+Dh56Fk4l99em1MTrDR06O3xWYLy/P7wqQDvQ1eOhZOJnYV59eG6MzfBC1tWdiDAypo6/BQ8/CycS+ErUFAABRwPABAAA8xfABAAA8FZ3hg6itPRNjYEgdfQ0eehZOJvbVp9fG6AwfAADACNEZPki72DPxTGykjr4GDz0LJxP7StoFAABEAcMHAADwFMMHAADwVHQWlgOAFLRqnLqUO+Dtx1bOdWOb8pOsEQiK6AwfRG3tmRgDQ+roa8paNU7j1erZ/va0PKIzPNsbPGPiY5FVbQHATIO9U5EOhzTc0/0BXovO8EHU1p6JMTCkjr4GDz0LJxP7StQWAABEAcMHAADwFMMHAADwVHTSLgBwkmI6rHFqTURlT+TYSal227xPkNYVTqLP5Xrfw4qQjOgMH0Rt7ZkYA0Pq6GvKJmi3WjU+5ftxGtntbOnQ2SnvLbycHMdxanWlZ64y8bFI1BYAws1pZDdDVporCTYnx3Gwd6Dgv+gMH0Rt7ZkYA0Pq6GvgjKko8rsEpIOJj0WitgAAIAoYPgAAgKcYPgAAgKeik3YBkDLijalJJrKLgTk5jqUi4WiypIaPtWvXau3atfrwww8lSRMmTNA//MM/aPbs2ZKknp4eLVmyRM8884wOHTqkmTNnas2aNSopKXG98KQRtbVnYgwMqXOpr4GNNxrEaWR3b8vDHlQTXG5Fnz1n4nNsEKK2JSUlWr58ubZt26Zt27bpkksu0ZVXXqldu3ZJkmpqarRhwwbV19dr8+bNOnjwoObMmaO+vr60FA/AO8QbvXOKDvldApBWSb3zMXfu3H4///jHP9batWu1detWlZSUaN26dXryySc1a9YsSdJTTz2l0tJSvfLKK7rsssvcq/pkELW1Z2IMDKmjr4EzpqLQ7xKQDiY+FoMWte3r61N9fb26u7s1bdo0NTc3q7e3V9XV1YltiouLNXHiRG3ZsmXA++np6VE8Hu93AQAA4ZX08NHS0qIRI0YoFovptttu04YNG/TVr35VHR0dys7O1siRI/ttX1BQoI6OjgHvr66uTvn5+YlLaWlp8v8KAAAQGEmnXc466yzt2LFDn3/+uZ577jnNmzdPmzZtGnB7y7KUkZEx4O1Lly7VokWLEj/H43EGEMMFMfEQxJpNQ8IAgFuSHj6ys7M1btw4SdLUqVPV1NSkhx56SNdee62OHDmi/fv393v3o7OzU5WVlQPeXywWUywWO4nSk0TaxZ6DM7GDmHgIYs2ucukM+8AmDILIxFQEUmdiX4OQdjkRy7LU09OjKVOmKCsrSw0NDYnb2tvbtXPnzkGHD890d/tdgfkcnG8TxMRDEGt2FedRBQ89CycT++rTa2NS73zcfffdmj17tkpLS9XV1aX6+no1NjbqpZdeUn5+vm655RYtXrxYp556qkaNGqUlS5aooqIikX7xVU6O3xWYLy/P7wqQDvQ1eOhZOJnYV59eG5MaPj755BPdeOONam9vV35+viZNmqSXXnpJl156qSRp5cqVyszM1DXXXJP4krH169dr6NChaSk+KURt7ZkYA0Pq6Gvw0LNwMrGvPr02JjV8rFu3btDbhw0bplWrVmnVqlUpFQUAAMKLheUAAICnWFgOSQli3DKINQNAmEVn+CBqa89BDCyIccsg1uwqE+N9GBw9CycT+xrUqC0AAEAyojN8kHaxZ+KZ2EgdfQ0eehZOJvY1aAvLAQAAnAyGDwAA4CmGDwAA4CmGDwAA4KnoDB9Ebe2ZGAND6uhr8NCzcDKxrz69NkZn+AAAAEaIzvBB1NaeiTEwpI6+Bg89CycT+0rUFgAARAHDBwAA8BTDBwAA8FR0FpaDa1o1Tl3KHfD2XHWpXO97WBEAIEiiM3wQtbXnIAbWqnEar9ZBtxmn1mivImsaE+N9GBw9CycT+8qqtgiCwd7xOCZXXR5UAgAIqugMH0Rt7ZkYA0Pq6Gvw0LNwMrGvRG0BAEAUMHwAAABPMXwAAABPRSftEnHO4rH2YjqscWod9KTSUjlLFhHZBYBois7wEeGorZN4rCTtaXlEZ9hsM0G7XYnREtn1kInxPgyOnoWTiX0laot0cRKPlaRDGp7mSv6AyC4ARFd0hg+itvZMjIEhdfQ1eOhZOJnYV6K2AAAgChg+AACAp6JzwmmEOUmoOD0vRHKWUrG7z30qtd3PYcUc1wQACI7oDB8RTrs4TajsbXnYdhunyRk39Crbk/2Enoln2GNw9CycTOwraZc06+72uwLjZcb/n+02ybxDkirSLi6Jx/2uAMmiZ+FkYl99em2MzvCRk+N3BcbLzvMuagsP5eX5XQGSRc/CycS++vTaGJ3hg6itrTEVhX6XgHQwMd6HwdGzcDKxr0RtAQBAFDB8AAAAT0Un7QJXJBPbTXUbpwvUAQgOFpSEFKXhI8JRW8ccxMDcWlgOHjIx3ofBhbRnkV9Q0sS+ErUFAIQZC0rimOgMH6Rd7Jl4JjZSR1+Dh56Fk4l9Je0CAACigOEDAAB4iuEDAAB4KjppFwCAr5xE9cMesSdq/KXoDB9Ebe2ZGAND6uhr8IS0Z1GP6re2HDYvakzUFgCA8CJq/AfRGT6I2tozMQaG1NHX4KFn4WRiX4naAgCAKGD4AAAAnmL4AAAAnopO2gUAAJ9FPWp8THSGD6K29kIa74s8+ho89CyUclveUqu+63cZ/RG1BQAgvEbooN8lGCM6wwdRW3smxsCQOvoaPPQslIoqxvhdwvGI2gIAgChg+AAAAJ5i+AAAAJ6KTtoFAEKGFVIRVEm981FXV6evfe1rys3N1WmnnaarrrpKv/nNb/pt09PTozvuuEOjR49WTk6OrrjiCn300UeuFn1SiNraI94XTvQ1eBz0rFXjNF6tmqLtA16+oX/3oFg4ZuJj0afXxqSGj02bNmnBggXaunWrGhoa9MUXX6i6ulrd3d2JbWpqarRhwwbV19dr8+bNOnjwoObMmaO+vj7XiweAqGKFVARZUh+7vPTSS/1+fvzxx3XaaaepublZF198sQ4cOKB169bpySef1KxZsyRJTz31lEpLS/XKK6/osssuc6/yZBG1tUe8L5zoa/DQs3Aysa9BjNoeOHBAkjRq1ChJUnNzs3p7e1VdXZ3Ypri4WBMnTtSWLVtOeB89PT2Kx+P9LgAAILxOeviwLEuLFi3ShRdeqIkTJ0qSOjo6lJ2drZEjR/bbtqCgQB0dHSe8n7q6OuXn5ycupaWlJ1sSAAAIgJNOuyxcuFDvvfeeNm/ebLutZVnKyMg44W1Lly7VokWLEj/H43EGEACwEdNhFilDYJ3U8HHHHXfoV7/6ld544w2VlJQkri8sLNSRI0e0f//+fu9+dHZ2qrKy8oT3FYvFFIvFTqaM5JB2sWfimdhIHX0NHgc9m6DdatV4D4qBa0x8LAZhYTnLsrRw4UI9//zzeu2111RWVtbv9ilTpigrK0sNDQ2J69rb27Vz584Bhw/P/FEiBwPgfJtwoq/BQ8/CycS++vTamNQ7HwsWLNDTTz+tF154Qbm5uYnzOPLz8zV8+HDl5+frlltu0eLFi3Xqqadq1KhRWrJkiSoqKhLpF9/k5Pi7/yDIy/O7AqQDfQ0eehZOJvbVp9fGpIaPtWvXSpKqqqr6Xf/4449r/vz5kqSVK1cqMzNT11xzjQ4dOqSZM2dq/fr1Gjp0qCsFnzSitvZMjIEhdfQ1eOhZOJnYV59eG5MaPizLst1m2LBhWrVqlVatWnXSRQEAgPBiYTkAAOApFpY7CSzm5A6Oo3ecHGtp8K/sdroNPQNSE4XnxugMHy5FbY8t5jSYcWoNZgTOwxhYqI+jYVpbDtsea7fQM5eYGMlE6pJYMHAwrj7OghC1BYs5uYXj6B0nx9ot9AxITVSeG6MzfJB2sWfimdhIHX0NHnoWTib2NYgLywEAAPxcleoAABOpSURBVCSL4QMAAHiK4QMAAHgqOmkXh+wiTvtUykqSLmBFTm/ZHesu5ep9lad8P/QMGByvMV+KzvDhIGob+finh/E+VuT0Tm7LW2rVdwfdJvJ/+6YhahtKTmLvnj/OiNr6LyoRJ0TLCB203Ya/fSD9eJz9QXSGD6K29kyMgSFlRRVj/C4ByeKxGE4m9pWoLQAAiAKGDwAA4CmGDwAA4KnopF0ciOmw7TaHFfOgEsBbRJ+942zFUoQVj7MvRWf4cBC1zVav7Ta9ynajGjMR7wsnB30l+uwNJ5FmSdrT8ojOSH858JiT2LvniNr6jxgUgHRyusLwIQ1PcyXwg5PYe1REZ/ggamvPxBgYUkdfg4eehZKRsXeitgAAIAoYPgAAgKcYPgAAgKeik3ZxgLghgHRy8hxz7KRUZ5Hc912vEeFhcqw7OsOHg6ht5OOGRG3Dib4aw+lzzCstG3WpaaufInUePhadxrp/u2+Xyr1P2vKxCwCYps/B/xcS+8dgnMa6nW7ntugMH0Rt7RHvCyf6GjhjKgr9LgHpYOJjkagtAACIAoYPAADgqeiccArjcDa/dzjWwUPyDqlwnqzyJ+8SneHDQdol8gw7E5uz+d3R2nKYYx0wRi5AhtR5+BzrNFm1a99vpXO9H0Ci87FLd7ffFZgvHvdsVyzi552uuGW7DcfaLJnx/X6XgHTw8DnWqSHd/jz2ozN85OT4XYH58vL8rgDpQF8DZ1helt8lIB0MfCz69dIYneGDqK09E2NgSB19DRwjVz9F6gx8LPr10hid4QMAABiB4QMAAHgqOmkXGIVF/LzFsTaHyYt9AV6JzvBB1NaegTEwpI7YpjmcLva1p+URnZH+cuA1Exd53LdPOtf7leX42AUIuRE66HcJ+D9OF/E6pOFprgTwV3SGD9Iu9gw8ExupIzkRQDwWw8nEvrKwHAAAiAKGDwAA4CmGDwAA4KnopF0ARJKTaKs0+Mmgbq3663ylUSDcojN8ELW1Z2IMDKmLcF+dRlvtuLXqr9OI+d6Wh1PeFwxk4mORqC0AuMutdxG8XvX3FB3ydH+A16IzfBC1tWdiDAypo6+BM6ai0O8SkA4mPhaJ2gIAgChg+AAAAJ5i+AAAAJ6KTtoFnjIp3mgit46Pk23KHe4vjMc6mWirV6v+sqotEKXhg6itPZdiYKbFG03j1vFxamPLq6q22V9Yj7Vpqyezqm3EEbVN4GMXuC6o8UaveP0lUp2yX1gurMfaNKxqC3wpOsMHUVt7JsbAkLqKSX5XgGTxWAwnE/tK1BYAAEQBwwcAAPAUwwcAAPBUdNIucI1dVHCfSl3Zz2HFXLkf07gV/3S+Tbnt/tyMkmJgrGoLfCnp4eONN97QP/3TP6m5uVnt7e3asGGDrrrqqsTtlmXpRz/6kR577DHt379f5513nh5++GFNmDDB1cKTRtTWnoMYmJcx0V5le7Ifr3kd/3y1ZaNaVe3Z/jAwVrWNOKK2CUl/7NLd3a3Jkydr9erVJ7x9xYoVeuCBB7R69Wo1NTWpsLBQl156qbq6iPKFgZf/V0b80x1j1Ol3CUgSq9oi7JJ+52P27NmaPXv2CW+zLEsPPvigli1bpquvvlqS9MQTT6igoEBPP/20vve976VWbSqI2tozMQaGlE2irYHDqrYhZeJzbBiitnv27FFHR4eqq//wFm8sFtP06dO1ZcuWE/5OT0+P4vF4vwsAAAgvV4ePjo4OSVJBQUG/6wsKChK3/am6ujrl5+cnLqWl7pysCAAAzJSWtEtGRka/ny3LOu66Y5YuXapFixYlfo7H4wwgBvMyqUECA0ET1QX8gGS5OnwUFn75OWVHR4eKiooS13d2dh73bsgxsVhMsZgHkUrSLvYcnIlt2kJdcMDEM+xDyEkSzPECfvQsnEzsa1DSLoMpKytTYWGhGhoaEtcdOXJEmzZtUmVlpZu7Sl53t7/7DwLOtwkn+uoJJ0kwxwkuehZOJvbVp9fGpN/5OHjwoN5//w9vG+7Zs0c7duzQqFGjdPrpp6umpkb33XefysvLVV5ervvuu0+nnHKKvvOd77haeNJycvzdfxDk5fldAdKBvgYPPQsnE/vq02tj0sPHtm3bNGPGjMTPx87XmDdvntavX6+77rpLhw4d0u233574krGNGzcqN9fnb+0jamvPxBgYUkdfg4eehZOJffXptTHp4aOqqkqWZQ14e0ZGhmpra1VbW5tKXQAAIKRYWA4AAHiKheUAwAVOYujEx50hshx+0Rk+iNraMzEGhtTRV0+4GkOPcM9cjSybxsS+hiFqCwBAKlyNLMNY0Rk+SLvYM/FMbKSOvgYPPQsnE/sahoXlAAAA7DB8AAAATzF8AAAAT0Un7QJgUE7ijdLgJwQ63YaYJAZCZDkaojN8ELW1Z2IMDKlz0Fcn8Ua3BDYm6aUIPxZDvXK2iX0lagvAL07ijW4hJgkgOsMHUVt7JsbAkDr6Gjz0LJxM7CtRWwAAEAUMHwAAwFMMHwAAwFPRSbuEmNcrQLLiZPg4iTd2KVfvq9z2vohJArATneEjpFFbV1eAdCmSSZTSMA766iTeSO89ZGIkE6kzsa9EbXEyvF4BkhUno4veA3BLdIYPorb2TIyBIXX0NXjoWTiZ2FeitgAAIAoYPgAAgKcYPgAAgKeik3YJKa9XgIzpsO02hxUjjhtCrDbqLR5DCLPoDB8hjdq6ugKkgxhYtnptt9mtCUQyTeJSvC/Uq40aprXlMI+hMCJqm8DHLkiKW6ufEskEBkasGWEXneGDqK09E2NgSB19DR56Fk4m9pWoLQAAiAKGDwAA4KnonHAKVzhdgEwa/DNpUhFAag4r5ncJwEmLzvAR0rSLq1xagAyGMfEMewyqo6VT0tmDbtOrbG+KgXtMfCySdkmz7m6/KzBfPO53BUgH+ho4h+Jf2G5D2iWATHws+vTaGJ3hIyfH7wrMl5fndwVIB/oaOMPysvwuAelg4mPRp9fG6AwfRG3tmRgDQ+roa+AUVYzxuwSkg4mPRaK2AAAgChg+AACAp6KTdgGAAAniIn4shgenojN8ELW1Z2IMDKmjr4GT2/KWWvVdv8tISqvGsRieHRMfi0RtAQCSNEIH/S4haSyGh2REZ/gg7WLPxDOxkTr6GjikXULKxMciaRcAABAFDB8AAMBTDB8AAMBT0Um7AADSxsmK1ybGg+GP6AwfRG3tmRgDQ+roa/AEsGeseO2AiX0lagsAAKIgOsMHUVt7JsbAkDr6Gjz0LJxM7CtRWwAAEAUMHwAAwFMMHwAAwFMMHwAAwFPRGT6I2tozMQaG1NHX4KFn4WRiX316bYzO8AEAAIwQneGDqK09E2NgSB19DR56Fk4m9pWoLQAAiAKGDwAA4CmGDwAA4KnoDB+kXeyZeCY2Ukdfg4eehZOJfQ1b2mXNmjUqKyvTsGHDNGXKFL355pvp2pUz3d3+7j8I4nG/K0A60NfgoWfhZGJffXptTMvw8eyzz6qmpkbLli3TO++8o4suukizZ8/WPj/ffcjJ8W/fQZGX53cFSAf6Gjz0LJxM7KtPr41pGT4eeOAB3XLLLbr11lt19tln68EHH1RpaanWrl173LY9PT2Kx+P9LmlB1NaeiTEwpI6+Bg89CycT+xqWqO2RI0fU3Nys6urqftdXV1dry5Ytx21fV1en/Pz8xKW0tNTtkgAAgEFcHz4+/fRT9fX1qaCgoN/1BQUF6ujoOG77pUuX6sCBA4lLW1ub2yUBAACDZKbrjjMyMvr9bFnWcddJUiwWUywWS1cZAADAMK6/8zF69GgNHTr0uHc5Ojs7j3s3BAAARI/rw0d2dramTJmihoaGftc3NDSosrLS7d05l5vr376D4rTT/K4A6UBfg4eehZOJffXptTEtH7ssWrRIN954o6ZOnapp06bpscce0759+3TbbbelY3fOlJdLv/2t1NU18DbHmhDVbThG4dyGvgZvG3oWzm1M7Gt5+cC3p1Faho9rr71Wn332mf7xH/9R7e3tmjhxov793/9dY8eOTcfunPPpIAcKxyic6Gvw0LNwoq+SpAzLsiy/i/hj8Xhc+fn5OnDggPJM/EIWAABwnGRev6OztgsAADACwwcAAPAUwwcAAPAUwwcAAPAUwwcAAPAUwwcAAPAUwwcAAPAUwwcAAPAUwwcAAPAUwwcAAPAUwwcAAPBUWhaWS8WxpWbi8bjPlQAAAKeOvW47WTLOuOGj6/+W/y0tLfW5EgAAkKyuri7l5+cPuo1xq9oePXpUH3/8sXJzc5WRkZG2/cTjcZWWlqqtrY3Vc9OMY+0NjrN3ONbe4Vh7J9VjbVmWurq6VFxcrCFDBj+rw7h3PoYMGaKSkhLP9peXl8cftEc41t7gOHuHY+0djrV3UjnWdu94HMMJpwAAwFMMHwAAwFNDa2tra/0uwi9Dhw5VVVWVMjON+/QpdDjW3uA4e4dj7R2OtXe8OtbGnXAKAADCjY9dAACApxg+AACApxg+AACApxg+AACApxg+AACApyI5fKxZs0ZlZWUaNmyYpkyZojfffNPvkgLvjTfe0Ny5c1VcXKyMjAz98pe/7He7ZVmqra1VcXGxhg8frqqqKu3atcunaoOtrq5OX/va15Sbm6vTTjtNV111lX7zm9/026anp0d33HGHRo8erZycHF1xxRX66KOPfKo4uNauXatJkyYlvvFx2rRp+o//+I/E7Rzn9Kirq1NGRoZqamoS13Gs3VFbW6uMjIx+l8LCwsTtXj1XR274ePbZZ1VTU6Nly5bpnXfe0UUXXaTZs2dr3759fpcWaN3d3Zo8ebJWr159wttXrFihBx54QKtXr1ZTU5MKCwt16aWXJhYShHObNm3SggULtHXrVjU0NOiLL75QdXW1uru7E9vU1NRow4YNqq+v1+bNm3Xw4EHNmTNHfX19PlYePCUlJVq+fLm2bdumbdu26ZJLLtGVV16ZeDLmOLuvqalJjz32mCZNmtTveo61eyZMmKD29vbEpaWlJXGbZ8/VVsR8/etft2677bZ+133lK1+xfvCDH/hUUfhIsjZs2JD4+ejRo1ZhYaG1fPnyxHWHDx+28vPzrUceecSPEkOls7PTkmRt2rTJsizL+vzzz62srCyrvr4+sc3vfvc7a8iQIdZLL73kV5mhMXLkSOtnP/sZxzkNurq6rPLycquhocGaPn26deedd1qWxd+0m+655x5r8uTJJ7zNy+fqSL3zceTIETU3N6u6urrf9dXV1dqyZYtPVYXfnj171NHR0e+4x2IxTZ8+nePuggMHDkiSRo0aJUlqbm5Wb29vv+NdXFysiRMncrxT0NfXp/r6enV3d2vatGkc5zRYsGCBLr/8cs2aNavf9Rxrd7W2tqq4uFhlZWW67rrr9MEHH0jy9rk6Ut9V++mnn6qvr08FBQX9ri8oKFBHR4dPVYXfsWN7ouO+d+9eP0oKDcuytGjRIl144YWaOHGipC+Pd3Z2tkaOHNlvW/7OT05LS4umTZumw4cPa8SIEdqwYYO++tWvaseOHRxnF9XX12v79u1qamo67jb+pt1z3nnn6ec//7nGjx+vTz75RPfee68qKyu1a9cuT5+rIzV8HJORkdHvZ8uyjrsO7uO4u2/hwoV67733tHnzZtttOd4n56yzztKOHTv0+eef67nnntO8efO0adOmAbfnOCevra1Nd955pzZu3Khhw4Y5/j2OdfJmz56d+O+KigpNmzZNZ555pp544gmdf/75krx5ro7Uxy6jR4/W0KFDj5uUOzs7j5v04J5jZ1Jz3N11xx136Fe/+pVef/11lZSUJK4vLCzUkSNHtH///n7bc7xPTnZ2tsaNG6epU6eqrq5OkydP1kMPPcRxdlFzc7M6Ozs1ZcoUZWZmKjMzU5s2bdI///M/KzMzUwUFBRzrNMnJyVFFRYVaW1s9fa6O1PCRnZ2tKVOmqKGhod/1DQ0Nqqys9Kmq8CsrK1NhYWG/437kyBFt2rSJ434SLMvSwoUL9fzzz+u1115TWVlZv9unTJmirKysfse7vb1dO3fu5Hi7wLIs9fT0cJxdNHPmTLW0tGjHjh2Jy9SpU3X99dcn/ptjnR49PT3avXu3ioqKvH2udvX01QCor6+3srKyrHXr1lm//vWvrZqaGisnJ8f68MMP/S4t0Lq6uqx33nnHeueddyxJ1gMPPGC988471t69ey3Lsqzly5db+fn51vPPP2+1tLRY3/72t62ioiIrHo/7XHnwfP/737fy8/OtxsZGq729PXH5/e9/n9jmtttus0pKSqxXXnnF2r59u3XJJZdYkydPtr744gsfKw+epUuXWm+88Ya1Z88e67333rPuvvtua8iQIdbGjRsty+I4p9Mfp10si2PtlsWLF1uNjY3WBx98YG3dutWaM2eOlZubm3gN9Oq5OnLDh2VZ1sMPP2yNHTvWys7Ots4999xERBEn7/XXX7ckHXeZN2+eZVlfRrjuueceq7Cw0IrFYtbFF19stbS0+Ft0QJ3oOEuyHn/88cQ2hw4dshYuXGiNGjXKGj58uDVnzhxr3759/hUdUDfffHPiuWLMmDHWzJkzE4OHZXGc0+lPhw+OtTuuvfZaq6ioyMrKyrKKi4utq6++2tq1a1fidq+eqzMsy7LcfS8FAABgYJE65wMAAPiP4QMAAHiK4QMAAHiK4QMAAHiK4QMAAHiK4QMAAHiK4QMAAHiK4QMAAHiK4QMAAHiK4QMAAHiK4QMAAHjq/wPC4PtjZ49vtgAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2316.0round= 22\n"
     ]
    }
   ],
   "source": [
    "T = 2\n",
    "Graph(40,50,T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Show Results\n",
    "Run the program with the parameter below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 800.0round= 1\n",
      "magnetization= 800.0round= 2\n",
      "magnetization= 800.0round= 3\n",
      "magnetization= 800.0round= 4\n",
      "magnetization= 798.0round= 5\n",
      "magnetization= 798.0round= 6\n",
      "magnetization= 796.0round= 7\n",
      "magnetization= 790.0round= 8\n",
      "magnetization= 784.0round= 9\n",
      "magnetization= 778.0round= 10\n",
      "magnetization= 768.0round= 11\n",
      "magnetization= 728.0round= 12\n",
      "magnetization= 666.0round= 13\n",
      "magnetization= 566.0round= 14\n",
      "magnetization= 418.0round= 15\n",
      "magnetization= 210.0round= 16\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 96.0round= 17\n"
     ]
    }
   ],
   "source": [
    "T = 2\n",
    "Graph(20,50,T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 3200.0round= 1\n",
      "magnetization= 3200.0round= 2\n",
      "magnetization= 3198.0round= 3\n",
      "magnetization= 3196.0round= 4\n",
      "magnetization= 3194.0round= 5\n",
      "magnetization= 3186.0round= 6\n",
      "magnetization= 3176.0round= 7\n",
      "magnetization= 3150.0round= 8\n",
      "magnetization= 3106.0round= 9\n",
      "magnetization= 3024.0round= 10\n",
      "magnetization= 2838.0round= 11\n",
      "magnetization= 2536.0round= 12\n",
      "magnetization= 1962.0round= 13\n",
      "magnetization= 1080.0round= 14\n",
      "magnetization= 264.0round= 15\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 12.0round= 16\n"
     ]
    }
   ],
   "source": [
    "T = 5 # Temperature\n",
    "Graph(40,50,T) # N=40, M=50\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1/T < (beta critical)  so magnetism tends to negative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 1800.0round= 1\n",
      "magnetization= 1800.0round= 2\n",
      "magnetization= 1800.0round= 3\n",
      "magnetization= 1800.0round= 4\n",
      "magnetization= 1800.0round= 5\n",
      "magnetization= 1800.0round= 6\n",
      "magnetization= 1800.0round= 7\n",
      "magnetization= 1792.0round= 8\n",
      "magnetization= 1778.0round= 9\n",
      "magnetization= 1776.0round= 10\n",
      "magnetization= 1760.0round= 11\n",
      "magnetization= 1712.0round= 12\n",
      "magnetization= 1624.0round= 13\n",
      "magnetization= 1466.0round= 14\n",
      "magnetization= 1360.0round= 15\n",
      "magnetization= 1246.0round= 16\n",
      "magnetization= 1042.0round= 17\n",
      "magnetization= 774.0round= 18\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 484.0round= 19\n"
     ]
    }
   ],
   "source": [
    "T = 2\n",
    "Graph(30,40,T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The magnetism tends to positive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetization= 39200.0round= 1\n",
      "magnetization= 39200.0round= 2\n",
      "magnetization= 39200.0round= 3\n",
      "magnetization= 39198.0round= 4\n",
      "magnetization= 39198.0round= 5\n",
      "magnetization= 39198.0round= 6\n",
      "magnetization= 39198.0round= 7\n",
      "magnetization= 39194.0round= 8\n",
      "magnetization= 39186.0round= 9\n",
      "magnetization= 39168.0round= 10\n",
      "magnetization= 39158.0round= 11\n",
      "magnetization= 39128.0round= 12\n",
      "magnetization= 39044.0round= 13\n",
      "magnetization= 38896.0round= 14\n",
      "magnetization= 38650.0round= 15\n",
      "magnetization= 38176.0round= 16\n",
      "magnetization= 37432.0round= 17\n",
      "magnetization= 36438.0round= 18\n",
      "magnetization= 35166.0round= 19\n",
      "magnetization= 34480.0round= 20\n",
      "magnetization= 33952.0round= 21\n",
      "magnetization= 33368.0round= 22\n"
     ]
    }
   ],
   "source": [
    "T = 2\n",
    "Graph(140,150,T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "state, before = runProppWilson(30,20,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "py\"Graph\"(before,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "py\"Graph\"(state,2)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.1.0",
   "language": "julia",
   "name": "julia-1.1"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.1.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}