Ising Project.ipynb

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  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating,visualizing and plotting data about an Ising model after learning about how it works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#pip install Pillow\n",
    "#pip install ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Imports\n",
    "\n",
    "import numpy as np\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",
    "from plotly.subplots import make_subplots\n",
    "import plotly.graph_objects as go\n",
    "from ipywidgets import interact\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is the length of one side of your grid?100\n",
      "What is the Coupling constant? 1 is most common. 1\n",
      "What is your Temperature from 0~6? For critical temperature type 22  22\n",
      "Critical temperature is given as 2 / log(1 + sqrt(2), e), or 2.269185314213022 and will be used for this system. \n"
     ]
    }
   ],
   "source": [
    "\n",
    "N=int(input('What is the length of one side of your grid?')) #Eg 50 makes a 50x50 grid\n",
    "M=N #Grid is even. playing with an uneven grid might be fun.\n",
    "\n",
    "J=int(input('What is the Coupling constant? 1 is most common. '))\n",
    "\n",
    "kT= float(input('What is your Temperature from 0~6? For critical temperature type 22  '))\n",
    "\n",
    "if kT==22:\n",
    "    \n",
    "    kT = 2 / log(1 + sqrt(2), e)#critical temp from Lars Onsangers solution\n",
    "    \n",
    "    print('Critical temperature is given as 2 / log(1 + sqrt(2), e), or', kT, 'and will be used for this system. ')\n",
    "\n",
    "\n",
    "Mag=[]#Places to store magnetization  values\n",
    "Energy=[] #Places to store energy values\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ================= create the random spin grid========================\n",
    "\n",
    "# Each spin has two possible states +1 or −1.\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": 5,
   "metadata": {},
   "outputs": [
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     "execution_count": 5,
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   "source": [
    "#=========Calculates Magnetization of the grid, which works out to be the summation of every point.======\n",
    "#If I were to rewrite this code having m= np.sum might lead to quicker times.\n",
    "\n",
    "\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 += Lattice[j,k]\n",
    "  \n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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     "execution_count": 6,
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   "source": [
    "#========================================= Calculating energy based on formula=================\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",
    "            Spin= Lattice[i, j] #choosen spin\n",
    "    \n",
    "    \n",
    "            SumOfNeighbors= (Lattice[(i+1)%N, (j)]#Right\n",
    "                     + Lattice[(i-1)%N, (j)]#left\n",
    "                     + Lattice[(i) , (j+1)%M]#Up\n",
    "                     + Lattice[(i) , (j-1)%M])#Down\n",
    "                     \n",
    "    \n",
    "            E+=J*Spin*SumOfNeighbors\n",
    "        \n",
    "    return E\n",
    "#Energy_Of_The_System(Grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#===================Using Energy calculation to find DeltaE and determine spin flips=====================\n",
    "\n",
    "\n",
    "\n",
    "def EnergyCalc(Lattice, i, j):\n",
    "    \n",
    "    \n",
    "    N, M = Lattice.shape #Giving my Lattice a size\n",
    "    \n",
    "    \n",
    "    Spin= Lattice[i, j] #choosen spin\n",
    "    \n",
    "    \n",
    "    SumOfNeighbors= (Lattice[(i+1)%N, (j)]#Right\n",
    "                     + Lattice[(i-1)%N, (j)]#left\n",
    "                     + Lattice[(i) , (j+1)%M]#Up\n",
    "                     + Lattice[(i) , (j-1)%M])#Down\n",
    "                     \n",
    "    \n",
    "    \n",
    "    \n",
    "    dE = (2*J)*(Spin*SumOfNeighbors) #Formula for dE\n",
    "                   \n",
    "                   \n",
    "    if dE <= 0 or exp(-dE / kT) > np.random.random(): #If dE <=0 or boltzmann factor greater than random swtich\n",
    "        Lattice[i, j] *= -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 13,
   "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": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the other way to do this without ipywidgets was just to call 'for i in range(frames)'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#In the following part-\n",
    "#Used Jake Vanderplas' visualization tutorial https://jakevdp.github.io/blog/2017/12/11/live-coding-cython-ising-model/\n",
    "\n",
    "\n",
    "#----------------------Visualize the Grid-------------------------------\n",
    "def Visualize(Lattice):\n",
    "    return Image.fromarray(np.uint8((Lattice + 1) * 0.5 * 255))  # 0 ... 255 Must be an 8 bit unsigned integer\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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       "interactive(children=(IntSlider(value=25, description='frame', max=50), Output()), _dom_classes=('widget-inter…"
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   ],
   "source": [
    "N_Frames=50\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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       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
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       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "FrameList=np.arange(0,len(Energy),1)\n",
    "\n",
    "fig = make_subplots(\n",
    "    rows=1, cols=2,\n",
    "    specs=[[{\"type\": \"bar\"}, {\"type\": \"pie\"}],#I didn't change these. These specs 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"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
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   "source": []
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   "execution_count": null,
   "metadata": {},
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   "source": []
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   "execution_count": null,
   "metadata": {},
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   "source": []
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