Infinite Range Ising.ipynb

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  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The infinite ising model- Juliano E."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#pip install Pillow\n",
    "#pip install ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "from math import exp, log, e, sqrt\n",
    "from ipywidgets import interact\n",
    "from PIL import Image\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "N=200 #Length of the system\n",
    "\n",
    "\n",
    "M=N #Grid is even..\n",
    "\n",
    "\n",
    "A=N**2#this relates to the number of particles in the system\n",
    "\n",
    "\n",
    "\n",
    "J=1/A\n",
    "\n",
    "\n",
    "\n",
    "kT=1e4     #unknown crit\n",
    "h=0\n",
    "Mag=[]\n",
    "Energy=[]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ================= create the random spin grid========================\n",
    "\n",
    "# Each spin has two possible states +1 or −1.\n",
    "\n",
    "\n",
    "\n",
    "def Initial_Lattice(N,M):\n",
    "    Spinvalues=[-1,1]\n",
    "    return np.random.choice(Spinvalues, size=(N, M))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#Here we save it so we can do some calculations from the starting point.\n",
    "\n",
    "Grid=Initial_Lattice(N,M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "#=========Calculates Magnetization of the grid based on the formula  ΣSi======\n",
    "\n",
    "def magnetization(Lattice):\n",
    "    m = 0.0  \n",
    "    for j in range(0,N):\n",
    "        for k in range(0,M):  \n",
    "            m += J*Lattice[j,k]\n",
    "  \n",
    "    return m"
   ]
  },
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   "execution_count": 55,
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   "source": [
    "#E=-1/2 Σ Jij, Si, Sj - Σ Hi, Si\n",
    "\n",
    "\n",
    "def Energy_Of_The_System(Lattice):\n",
    "    E=0.0\n",
    "  \n",
    "    \n",
    "    for i in range(0,N):\n",
    "        for j in range(0,M):\n",
    "            \n",
    "            \n",
    "            \n",
    "            Spin= Lattice[i, j] \n",
    "            \n",
    "    \n",
    "            SumOfNeighbors= np.sum(Lattice) -Lattice[i, j] \n",
    "                     \n",
    "    \n",
    "            E+=(0.5*J*Spin*SumOfNeighbors)- (h*Spin)\n",
    "        \n",
    "    #print('The total energy of the system is', E)\n",
    "    return E\n",
    "Energy_Of_The_System(Grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "#===============P(σ)=exp[−∑h*σ − 1/2 ∑i,jJijσiσj]\n",
    "\n",
    "#\n",
    "\n",
    "\n",
    "def EnergyCalc(Lattice, i, j):\n",
    "    \n",
    "\n",
    "    \n",
    "    N, M = Lattice.shape\n",
    "    \n",
    "    \n",
    "    Spin= Lattice[i, j] \n",
    "    \n",
    "    SumOfNeighbors= np.sum(Lattice) -Lattice[i, j] \n",
    "            \n",
    "    dE = (0.5*2*J)*((Spin*SumOfNeighbors) - (h*Spin))\n",
    "                   \n",
    "                   \n",
    "    if dE <= 0 or exp(-dE/kT) > np.random.random():\n",
    "        Lattice[i, j] *= -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "#=================================== Movement through the lattice ==============\n",
    "#This is the simplest case, but experimenting with other iterations over the grid can lead to changed results.\n",
    "\n",
    "#I've found going randomly across the lattice caused the grid to continue to be random. \n",
    "#there might be a proper way to do this, but I've not found it.\n",
    "\n",
    "#The coordinates of this movement type for a 3x3 Lattice is commented in the cell below if interested. \n",
    "\n",
    "\n",
    "def Movement(Lattice):\n",
    "    N, M = Lattice.shape\n",
    "\n",
    "    for i in range(N):\n",
    "        for j in range(M): \n",
    "            EnergyCalc(Lattice, i, j)\n",
    "            \n",
    "#=========== Calls and saves values for measurements while the grid is being updated============            \n",
    "            \n",
    "    Mag.append(magnetization(Lattice))\n",
    "    Energy.append(Energy_Of_The_System(Lattice))\n",
    "    return Lattice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "#X_Coordinates=[0, 1, 2, 0, 1, 2, 0, 1, 2]\n",
    "#Y_Coordinates=[0, 0, 0, 1, 1, 1, 2, 2, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "#----------------------Visualize the Grid-------------------------------Thanks to https://jakevdp.github.io/blog/2017/12/11/live-coding-cython-ising-model/ for the visualization tutorial\n",
    "def Visualize(Lattice):\n",
    "    return Image.fromarray(np.uint8((Lattice + 1) * 0.5 * 255))  # 0 ... 255\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 60,
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   "source": [
    "N_Frames=50 #Number of frames NOTE: ANYTHING OVER 50 TAKES SOME TIME RUN.\n",
    "\n",
    "from ipywidgets import interact\n",
    "\n",
    "def Evolution(images):\n",
    "    \n",
    "    \n",
    "    def show(frame=(0, len(images)-1)):\n",
    "        \n",
    "        \n",
    "        return Visualize(images[frame])\n",
    "    \n",
    "    \n",
    "    return interact(show)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "images = [Grid]\n",
    "\n",
    "\n",
    "for i in range(N_Frames):\n",
    "    \n",
    "    images.append(Movement(images[-1].copy()))\n",
    "    \n",
    "Evolution(images);"
   ]
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   "source": [
    "\n",
    "FrameList=np.arange(0,len(Energy),1)\n",
    "\n",
    "from plotly.subplots import make_subplots\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "fig = make_subplots(\n",
    "    rows=1, cols=2,\n",
    "    specs=[[{\"type\": \"bar\"}, {\"type\": \"pie\"}],#I Don't know the correct type, these just happend to work. Others don't\n",
    "           ],\n",
    ")\n",
    "\n",
    "#Each fig.add_trace is a new graph\n",
    "#Making traces on the same row and col allow them to be plotted together. \n",
    "\n",
    "\n",
    "#traces for Energy and Magnetization\n",
    "fig.add_trace(go.Scatter(y=(Energy), name='Energy points(J)', mode='lines', marker_color='red'),row=1,col=1)\n",
    "fig.add_trace(go.Scatter(y=(Mag), name='Magnetization(T)', mode='lines', marker_color='orchid'),row=1,col=1)\n",
    "fig.update_layout(title='Evolution Data of The Ising Model',\n",
    "                   xaxis_title='Frames',\n",
    "                   yaxis_title='Quantity')\n",
    "\n",
    "#Trace for the table\n",
    "fig.add_trace(go.Table(\n",
    "    header=dict(values=['Frame #','Energies', 'Magnetizations'],\n",
    "                line_color='darkslategray',\n",
    "                fill_color='lightskyblue',\n",
    "                align='left'),\n",
    "    cells=dict(values=[FrameList,Energy, Mag], # 2nd column\n",
    "               line_color='darkslategray',\n",
    "               fill_color='lightcyan',\n",
    "               align='left')),row=1,col=2)            \n",
    "\n",
    "fig.update_layout(width=1000, height=500, showlegend=True)\n",
    "\n",
    "fig.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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