Ising_tensorflow_v2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FUXq3VEkNvHj"
   },
   "source": [
    "# Ising model Monte-Carlo with Metropolis Checkerboard update on Tensorflow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cellView": "form",
    "id": "t14f3pYHNvHr"
   },
   "outputs": [],
   "source": [
    "#@title Imports\n",
    "import numpy as np\n",
    "import tensorflow as tf #(v2.4.0)\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display\n",
    "import time\n",
    "from platform import python_version\n",
    "mpl.rcParams['figure.facecolor'] = '#222222'\n",
    "mpl.rcParams['axes.facecolor'] = '#222222'\n",
    "mpl.rcParams['axes.labelcolor'] = '#edece9'\n",
    "mpl.rcParams['xtick.color'] = '#edece9'\n",
    "mpl.rcParams['ytick.color'] = '#edece9'\n",
    "mpl.rcParams['text.color'] = '#edece9' "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1fkGFgWsVzRo",
    "outputId": "591bca72-4087-4a71-aff8-bc2139a3eb5f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "python-3.7.9\n",
      "tensorflow==2.4.0\n",
      "matplotlib==3.3.3\n",
      "numpy==1.19.5\n",
      "ipywidgets==7.6.3\n"
     ]
    }
   ],
   "source": [
    "#@title Requirements\n",
    "print(\"python-\"+python_version())\n",
    "print(\"tensorflow==\"+tf.__version__)\n",
    "print(\"matplotlib==\"+mpl.__version__)\n",
    "print(\"numpy==\"+np.__version__)\n",
    "print(\"ipywidgets==\"+widgets.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "cellView": "form",
    "id": "64qmionZNvHs"
   },
   "outputs": [],
   "source": [
    "#@title Reset Model\n",
    "from tensorflow.python.framework import ops\n",
    "ops.reset_default_graph()\n",
    "print_shape = True \n",
    "DIMS = 2\n",
    "dims = DIMS\n",
    "BOUNDARY_CONDITION = [1]*DIMS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cellView": "form",
    "id": "uBEu6iFzNvHt"
   },
   "outputs": [],
   "source": [
    "#@title Boundary Condition\n",
    "@tf.function\n",
    "def shift_spin(x, axis=0, shift=0, bcaxis=1):    \n",
    "    shifted_x = x\n",
    "    # dims = tf.rank(x)\n",
    "    if shift==1:\n",
    "        perm = tf.range(start=0, limit=dims, delta=1)\n",
    "        permd = tf.sparse.to_dense(tf.sparse.SparseTensor([[0],[axis]], [axis,-axis], [dims]))\n",
    "        perm = perm + permd\n",
    "        if axis>0:\n",
    "            shifted_x = tf.transpose(shifted_x, perm)\n",
    "        shifted_x = tf.concat([shifted_x[1:], bcaxis*shifted_x[:1]], axis=0)\n",
    "        if axis>0:\n",
    "            shifted_x = tf.transpose(shifted_x, perm)\n",
    "    if shift==-1:\n",
    "        perm = tf.range(start=0, limit=dims, delta=1)\n",
    "        permd = tf.sparse.to_dense(tf.sparse.SparseTensor([[0],[axis]], [axis,-axis], [dims]))\n",
    "        perm = perm + permd\n",
    "        if axis>0:\n",
    "            shifted_x = tf.transpose(shifted_x, perm)\n",
    "        shifted_x = tf.concat([bcaxis*shifted_x[-1:], shifted_x[:-1]], axis=0)\n",
    "        if axis>0:\n",
    "            shifted_x = tf.transpose(shifted_x, perm)\n",
    "    return shifted_x\n",
    "# shift_spin(spin_input)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cellView": "form",
    "id": "_jigmNODNvHu"
   },
   "outputs": [],
   "source": [
    "#@title Potential\n",
    "@tf.function\n",
    "def potential_persite(x, uniformJ, uniformH, bc, print_shape=False):\n",
    "    potential = -uniformH + 0*x\n",
    "    # dims = tf.rank(x)\n",
    "    # while_condition = lambda axis: tf.less(axis, dims)\n",
    "    for axis in range(dims):\n",
    "        for s in [-1,1]:\n",
    "            potential = potential - uniformJ[axis]*shift_spin(x, axis=axis, shift=s, bcaxis=bc[axis])\n",
    "    \n",
    "    if print_shape: print(\"potential:\"+str(potential.shape))\n",
    "    return potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cellView": "form",
    "id": "mbmKenr2NvHv"
   },
   "outputs": [],
   "source": [
    "#@title Checkerboard update\n",
    "@tf.function\n",
    "def update(x, stncl, Temperature, uniformJ, uniformH, bc):\n",
    "    r = tf.random.uniform(tf.shape(x), minval=0, maxval=1, dtype=tf.float32)\n",
    "    dE = -2*x*stncl*potential_persite(x, uniformJ=uniformJ, uniformH=uniformH, bc=bc)\n",
    "    p = tf.where(dE<=0.0,stncl,stncl*tf.exp(-dE/Temperature))\n",
    "    y = tf.where(p>1-r,-x,x)\n",
    "\n",
    "    return y\n",
    "# update(spin_input,stencil)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "cellView": "form",
    "id": "ytshHL97NvHw"
   },
   "outputs": [],
   "source": [
    "#@title Measurement Step\n",
    "@tf.function\n",
    "def measure_step(x, stncl, Temperature, uniformJ, uniformH, bc, steps=1):\n",
    "    spinin = x\n",
    "    for i in range(steps):\n",
    "        # print(\"here!\")\n",
    "        y = update(spinin, stncl, Temperature, uniformJ, uniformH, bc)\n",
    "        # print(\"here!\")\n",
    "        spinin = update(y, 1-stncl, Temperature, uniformJ, uniformH, bc)\n",
    "        # print(f\"here! {i}\")\n",
    "    return spinin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cellView": "form",
    "id": "gwc-t_KVNvHw"
   },
   "outputs": [],
   "source": [
    "#@title Testing \n",
    "def initialize_stencil_spin(sshape, p=0.5):\n",
    "    gs = tf.random.Generator.from_non_deterministic_state()\n",
    "    spin_input = tf.where(gs.uniform(shape=sshape)<p,1.0,-1.0)\n",
    "    stencil = spin_input*0\n",
    "    for axis in range(len(sshape)):\n",
    "        stencil = tf.math.floormod(stencil + tf.cumsum(spin_input*0+1, axis=axis), 2)\n",
    "    # if print_shape: print(\"stencil:\"+str(stencil.shape))\n",
    "    return spin_input,stencil\n",
    "\n",
    "spin_input,stencil = initialize_stencil_spin([1000]*DIMS)\n",
    "\n",
    "spin_output = measure_step(x=spin_input, \n",
    "                           stncl=stencil, \n",
    "                           Temperature=tf.constant(2.27), \n",
    "                           uniformJ=tf.constant([1.0]*DIMS), \n",
    "                           uniformH=tf.constant(0.0), \n",
    "                           bc=tf.constant(BOUNDARY_CONDITION, tf.float32), \n",
    "                           steps=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cellView": "form",
    "id": "HBNQSWZjmu9k"
   },
   "outputs": [],
   "source": [
    "#@title Magnetization and Energy\n",
    "\n",
    "@tf.function\n",
    "def magnetization_per_site(x,moments=[1,2,3,4]):\n",
    "    magnetization = tf.reduce_mean(x)\n",
    "    magnetization_moments = [magnetization**i for i in moments]\n",
    "    return magnetization_moments\n",
    "\n",
    "@tf.function\n",
    "def energy_per_site(x, uniformJ, uniformH, bc, moments=[1,2,3,4]):\n",
    "    energy = -uniformH + 0*x\n",
    "    # dims = tf.rank(x)\n",
    "    # while_condition = lambda axis: tf.less(axis, dims)\n",
    "    for axis in range(dims):\n",
    "        energy = energy - uniformJ[axis]*shift_spin(x, axis=axis, shift=1, bcaxis=bc[axis]) \n",
    "    energy = energy*x\n",
    "    energy = tf.reduce_mean(energy)\n",
    "    energy_moments = [energy**i for i in moments]\n",
    "    return energy_moments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LXvz8iIUKfkG"
   },
   "source": [
    "# Interactive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cellView": "form",
    "id": "7rVaLSxF0xaB"
   },
   "outputs": [],
   "source": [
    "#@title Plot Update\n",
    "def show_plot(**kwargs):\n",
    "    global fig,axM,axE,axpin,gs,spin,energys,magnetization,MCS_steps\n",
    "    try:\n",
    "        plt.close();\n",
    "        fig = plt.figure(figsize=(16,8),constrained_layout=True)\n",
    "        gs = fig.add_gridspec(2, 4)\n",
    "        axM = fig.add_subplot(gs[0,0:2])\n",
    "        axE = fig.add_subplot(gs[1,0:2])\n",
    "        axpin = fig.add_subplot(gs[:,2:])\n",
    "    except:\n",
    "        fig = plt.figure(figsize=(16,8),constrained_layout=True)\n",
    "        gs = fig.add_gridspec(2, 4)\n",
    "        axM = fig.add_subplot(gs[0,0:2])\n",
    "        axE = fig.add_subplot(gs[1,0:2])\n",
    "        axpin = fig.add_subplot(gs[:,2:])\n",
    "    col = [\"#f58231\",\"#3cb44b\",\"#4363d8\",\"#911eb4\"]\n",
    "    mark = [\"s\",\"D\",\"^\",\"v\"]\n",
    "    axM.cla()\n",
    "    axE.cla()\n",
    "    axpin.cla()\n",
    "    # axM.set_xlabel(\"Monte-Carlo Steps\");\n",
    "    axM.set_ylabel(\"Magnetization\");\n",
    "    leg = False\n",
    "    for mi,mv in enumerate(show_Ms):\n",
    "        if mv.value:\n",
    "            axM.plot(MCS_steps,[m[mi] for m in magnetizations],c=col[mi],marker=mark[mi],linestyle='dotted',markersize=2,label=r\"$\"+mv.description+r\"$\")\n",
    "            leg = True\n",
    "    for mi,mv in enumerate(show_Mavgs):\n",
    "        if mv.value:\n",
    "            axM.plot(MCS_steps,np.cumsum([m[mi] for m in magnetizations])/np.arange(1,len(magnetizations)+1),c=col[mi],label=r\"$ \\langle \"+mv.description[1:-1]+r\" \\rangle $\")\n",
    "            leg = True\n",
    "    if leg:\n",
    "        axM.legend()\n",
    "    axE.set_xlabel(\"Monte-Carlo Steps\");\n",
    "    axE.set_ylabel(\"Energy\");\n",
    "    leg = False\n",
    "    for ei,ev in enumerate(show_Es):\n",
    "        if ev.value:\n",
    "            axE.plot(MCS_steps,[e[ei] for e in energys],c=col[ei],marker=mark[ei],linestyle='dotted',markersize=2,label=r\"$\"+ev.description+r\"$\")\n",
    "            leg = True\n",
    "    for ei,ev in enumerate(show_Eavgs):\n",
    "        if ev.value:\n",
    "            axE.plot(MCS_steps,np.cumsum([e[ei] for e in energys])/np.arange(1,len(energys)+1),c=col[ei],label=r\"$\\langle \"+ev.description[1:-1]+r\" \\rangle $\")\n",
    "            leg = True\n",
    "    if leg:\n",
    "        axE.legend()\n",
    "    axpin.set_title(\"MCS:\"+str(MCS_steps[-1]))\n",
    "    axpin.imshow(spin,vmin=-1,vmax=1)\n",
    "    axpin.axis('off')\n",
    "    # fig.canvas.draw();\n",
    "    # plt.pause(0.001)\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "cellView": "form",
    "id": "h_fA9-T3KXh0"
   },
   "outputs": [],
   "source": [
    "#@title Main Buttons\n",
    "init_but = widgets.Button(description=\"Re/Initialize\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'},\n",
    "                          button_style='success')\n",
    "def init_button(button_click):\n",
    "    global spin,stencil,energys,magnetizations,MCS_steps\n",
    "    # print(f\"\\rInitializing...                                    \",end=' ',flush=True)\n",
    "    status_text.value = f\"Initializing... \"\n",
    "    spin,stencil = initialize_stencil_spin([l.value for l in L_sliders],p=S_slider.value)\n",
    "    magnetizations = [magnetization_per_site(spin)]\n",
    "    energys = [energy_per_site(spin,uniformJ=[j.value for j in J_sliders],uniformH=H_slider.value,bc=[b.value for b in BC_sliders])]\n",
    "    MCS_steps = [0] \n",
    "    update_dict[\"Update\"].value = not update_dict[\"Update\"].value\n",
    "    # print(f\"\\rInitializing... Done!                              \",end=' ',flush=True)\n",
    "    status_text.value = f\"Initialized! \"\n",
    "init_but.on_click(init_button)\n",
    "\n",
    "sim_but = widgets.Button(description=\"Simulate\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'},\n",
    "                         button_style='success')\n",
    "def sim_button(button_click):\n",
    "    global spin,stencil,energys,magnetizations,MCS_steps\n",
    "    tStart = time.time()\n",
    "    for step in range(MCS_sliders[1].value):\n",
    "        # print(f\"\\rSimulating... {int(100*step/MCS_sliders[1].value)}% - {int(0.5+time.time()-tStart)} seconds\",end=' ',flush=True)\n",
    "        status_text.value = f\"Simulating... {int(100*step/MCS_sliders[1].value)}% - {int(0.5+time.time()-tStart)} seconds\"\n",
    "        spin = measure_step(x=spin, \n",
    "                            stncl=stencil, \n",
    "                            Temperature=tf.constant(T_slider.value), \n",
    "                            uniformJ=tf.constant([j.value for j in J_sliders]), \n",
    "                            uniformH=tf.constant(H_slider.value), \n",
    "                            bc=tf.constant([b.value for b in BC_sliders], tf.float32), \n",
    "                            steps=MCS_sliders[0].value)\n",
    "        magnetizations.append(magnetization_per_site(spin))\n",
    "        energys.append(energy_per_site(spin,uniformJ=[j.value for j in J_sliders],uniformH=H_slider.value,bc=[b.value for b in BC_sliders]))\n",
    "        MCS_steps.append(MCS_steps[-1]+MCS_sliders[0].value)\n",
    "        if (plot_period.value and (step+1)%plot_period.value==0) or (step+1)==MCS_sliders[1].value :\n",
    "            # show_plot()\n",
    "            update_dict[\"Update\"].value = not update_dict[\"Update\"].value\n",
    "    # print(f\"\\rSimulating...  {int(100)}% - {int(0.5+time.time()-tStart)} seconds\",end=' ',flush=True)\n",
    "    status_text.value = f\"Simulating...  {int(100)}% - {int(0.5+time.time()-tStart)} seconds\"\n",
    "sim_but.on_click(sim_button)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "cellView": "form",
    "id": "yMoRHn7baYxI"
   },
   "outputs": [],
   "source": [
    "#@title Buttons and Sliders\n",
    "S_slider = widgets.FloatSlider(value=0.5,\n",
    "                               min=0.0,\n",
    "                               max=1.0,\n",
    "                               step=0.01,\n",
    "                               description=\"p\",\n",
    "                               readout=True,\n",
    "                               style={'description_width': 'initial'},\n",
    "                               layout={'width':'auto'},\n",
    "                               continuous_update=False,\n",
    "                               orientation='horizontal'\n",
    "                              )\n",
    "\n",
    "T_slider = widgets.FloatSlider(value=2.27,\n",
    "                               min=0.01,\n",
    "                               max=9.99,\n",
    "                               step=0.01,\n",
    "                               description=\"T\",\n",
    "                               readout=True,\n",
    "                               style={'description_width': 'initial'},\n",
    "                               layout={'width':'auto'},\n",
    "                               continuous_update=False,\n",
    "                               orientation='horizontal'\n",
    "                              )\n",
    "\n",
    "J_sliders = [widgets.FloatSlider(value=1.0,\n",
    "                                 min=-2.0,\n",
    "                                 max=2.0,\n",
    "                                 step=0.01,\n",
    "                                 description=f\"J[{i}]\",\n",
    "                                 readout=True,\n",
    "                                 style={'description_width': 'initial'},\n",
    "                                 layout={'width':'auto'},\n",
    "                                 continuous_update=False,\n",
    "                                 orientation='horizontal'\n",
    "                                ) for i in range(DIMS)]\n",
    "\n",
    "H_slider = widgets.FloatSlider(value=0.0,\n",
    "                               min=-5.0,\n",
    "                               max=5.0,\n",
    "                               step=0.01,\n",
    "                               description=f\"H\",\n",
    "                               readout=True,\n",
    "                               style={'description_width': 'initial'},\n",
    "                               layout={'width':'auto'},\n",
    "                               continuous_update=False,\n",
    "                               orientation='horizontal'\n",
    "                              )\n",
    "\n",
    "L_sliders = [widgets.IntSlider(value=100,\n",
    "                               min=2,\n",
    "                               max=10000,\n",
    "                               step=2,\n",
    "                               description=f\"L[{i}]\",\n",
    "                               readout=True,\n",
    "                               style={'description_width': 'initial'},\n",
    "                               layout={'width':'auto'},\n",
    "                               continuous_update=False,\n",
    "                               orientation='horizontal'\n",
    "                              ) for i in range(DIMS)]\n",
    "\n",
    "BC_sliders = [widgets.FloatSlider(value=1,\n",
    "                                  min=-1,\n",
    "                                  max=1,\n",
    "                                  step=0.01,\n",
    "                                  description=f\"BC[{i}]\",\n",
    "                                  readout=True,\n",
    "                                  style={'description_width': 'initial'},\n",
    "                                  layout={'width':'auto'},\n",
    "                                  continuous_update=False,\n",
    "                                  orientation='horizontal'\n",
    "                                 ) for i in range(DIMS)]\n",
    "\n",
    "rnd_but = widgets.Button(description=\"p[Spin UP]=p[Spin DOWN]\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'})\n",
    "def rnd_button(button_click):\n",
    "    S_slider.value = 0.5\n",
    "rnd_but.on_click(rnd_button)\n",
    "sqr_but = widgets.Button(description=\"Equal Lattice dimensions: L[i]=L[0]\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'})\n",
    "def sqr_button(button_click):\n",
    "    for L_slider in L_sliders:\n",
    "        L_slider.value = L_sliders[0].value\n",
    "sqr_but.on_click(sqr_button)\n",
    "same_but = widgets.Button(description=\"Same Boundary condition: BC[i]=BC[0]\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'})\n",
    "def same_button(button_click):\n",
    "    for BC_slider in BC_sliders:\n",
    "        BC_slider.value = BC_sliders[0].value\n",
    "same_but.on_click(same_button)\n",
    "iso_but = widgets.Button(description=\"Isotropic Interactions: J[i]=J[0]\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'})\n",
    "def iso_button(button_click):\n",
    "    for J_slider in J_sliders:\n",
    "        J_slider.value = J_sliders[0].value\n",
    "iso_but.on_click(iso_button)\n",
    "h0_but = widgets.Button(description=\"Zero Field\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'})\n",
    "def h0_button(button_click):\n",
    "    H_slider.value = 0.0\n",
    "h0_but.on_click(h0_button)\n",
    "crt_but = widgets.Button(description=\"Critical Temperature\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'})\n",
    "def crt_button(button_click):\n",
    "    T_slider.value = 2.27\n",
    "crt_but.on_click(crt_button)\n",
    "\n",
    "def_but = widgets.Button(description=\"Default Parameters\",\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'},\n",
    "                         button_style='info')\n",
    "def def_button(button_click):\n",
    "    for BC_slider in BC_sliders:\n",
    "        BC_slider.value = 1\n",
    "    for J_slider in J_sliders:\n",
    "        J_slider.value = 1.0\n",
    "    H_slider.value = 0.0\n",
    "    T_slider.value = 2.27\n",
    "def_but.on_click(def_button)\n",
    "\n",
    "show_spin = widgets.ToggleButton(value=True,\n",
    "                                 description='Spin Configuration',\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'}\n",
    "                                )\n",
    "show_Ms = [widgets.ToggleButton(value=True,\n",
    "                               description=f\"M{s}\",\n",
    "                               layout={'width':'auto', 'height':'30px', 'align':'center'}\n",
    "                              ) for s in [\"\",\"^2\",\"^3\",\"^4\"] ]\n",
    "show_Mavgs = [widgets.ToggleButton(value=True,\n",
    "                               description=f\"<M{s}>\",\n",
    "                               layout={'width':'auto', 'height':'30px', 'align':'center'}\n",
    "                              ) for s in [\"\",\"^2\",\"^3\",\"^4\"] ]\n",
    "show_Es = [widgets.ToggleButton(value=True,\n",
    "                               description=f\"E{s}\",\n",
    "                               layout={'width':'auto', 'height':'30px', 'align':'center'}\n",
    "                              ) for s in [\"\",\"^2\",\"^3\",\"^4\"] ]\n",
    "show_Eavgs = [widgets.ToggleButton(value=True,\n",
    "                               description=f\"<E{s}>\",\n",
    "                               layout={'width':'auto', 'height':'30px', 'align':'center'}\n",
    "                              ) for s in [\"\",\"^2\",\"^3\",\"^4\"] ]\n",
    "MCS_sliders = [widgets.IntSlider(value=i/100,\n",
    "                                 min=1,\n",
    "                                 max=i,\n",
    "                                 step=1,\n",
    "                                 description=f\"{s}\",\n",
    "                                 readout=True,\n",
    "                                 style={'description_width': 'initial'},\n",
    "                                 layout={'width':'auto', 'height':'30px', 'align':'center'},\n",
    "                                 continuous_update=False,\n",
    "                                 orientation='horizontal'\n",
    "                                ) for s,i in [[\"Sampling Interval\",1000],[\"Number of Samples\",10000]] ]\n",
    "\n",
    "plot_period = widgets.ToggleButtons(options=[('after simulation Ends',0),('every 100th Interval',100),('every 10th Interval',10),('every Interval',1)],\n",
    "                                      description='Update Plot:',\n",
    "                                      disabled=False,\n",
    "                                      style={'button_width': 'auto'},\n",
    "                                      layout={'width':'auto', 'height':'30px', 'align':'center'},\n",
    "                                      button_style='warning',#'success', 'info', 'warning', 'danger' or ''\n",
    "                                      tooltips=['Recommended', 'Slow', 'Slower', 'Slowest'],\n",
    "                                      # icons=['check'] * 3\n",
    "                                   )\n",
    "\n",
    "update_dict = {\n",
    "    \"spin\": show_spin,\n",
    "    \"M1\": show_Ms[0],\n",
    "    \"M2\": show_Ms[1],\n",
    "    \"M3\": show_Ms[2],\n",
    "    \"M4\": show_Ms[3],\n",
    "    \"Mavg1\": show_Mavgs[0],\n",
    "    \"Mavg2\": show_Mavgs[1],\n",
    "    \"Mavg3\": show_Mavgs[2],\n",
    "    \"Mavg4\": show_Mavgs[3],\n",
    "    \"E1\": show_Es[0],\n",
    "    \"E2\": show_Es[1],\n",
    "    \"E3\": show_Es[2],\n",
    "    \"E4\": show_Es[3],\n",
    "    \"Eavg1\": show_Eavgs[0],\n",
    "    \"Eavg2\": show_Eavgs[1],\n",
    "    \"Eavg3\": show_Eavgs[2],\n",
    "    \"Eavg4\": show_Eavgs[3],\n",
    "    \"Update\": widgets.Checkbox(value=True,\n",
    "                               description='Update',\n",
    "                               disabled=False,\n",
    "                               button_style=''\n",
    "                              )\n",
    "}\n",
    "status_text = widgets.Text(\n",
    "    value='Initialized!',\n",
    "    placeholder='Paste ticket description here!',\n",
    "    description='Status:',\n",
    "    disabled=True,\n",
    "    layout={'width':'auto', 'height':'30px', 'align':'center'}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "cellView": "form",
    "id": "8Dw21yxPA5kb"
   },
   "outputs": [],
   "source": [
    "#@title Initialize for the first time\n",
    "spin,stencil = initialize_stencil_spin([l.value for l in L_sliders])\n",
    "magnetizations = [magnetization_per_site(spin)]\n",
    "energys = [energy_per_site(spin,uniformJ=[j.value for j in J_sliders],uniformH=H_slider.value,bc=[b.value for b in BC_sliders])]\n",
    "MCS_steps = [0]"
   ]
  },
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    "id": "Rck9kls-jwpd",
    "outputId": "fda484ff-f15d-4265-95b0-f0d48665141f",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7140a3adbf954c3aafe23e787acbb17e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output(layout=Layout(border='0px solid black'))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Main display\n",
    "L_accordian = widgets.Accordion(children=[widgets.VBox([sqr_but,*L_sliders])])\n",
    "L_accordian.set_title(0,'Lattice Dimensions')\n",
    "S_accordian = widgets.Accordion(children=[widgets.VBox([rnd_but,S_slider])])\n",
    "S_accordian.set_title(0,'Spin UP probability')\n",
    "init_tab = widgets.VBox([S_accordian,L_accordian,init_but])\n",
    "\n",
    "BC_accordian = widgets.Accordion(children=[widgets.VBox([same_but,*BC_sliders])])\n",
    "BC_accordian.set_title(0,'Boundary Conditions')\n",
    "J_accordian = widgets.Accordion(children=[widgets.VBox([iso_but,*J_sliders])])\n",
    "J_accordian.set_title(0,'Nearest-neighbor Interactions')\n",
    "H_accordian = widgets.Accordion(children=[widgets.VBox([h0_but,H_slider])])\n",
    "H_accordian.set_title(0,'Uniform Field')\n",
    "T_accordian = widgets.Accordion(children=[widgets.VBox([crt_but,T_slider])])\n",
    "T_accordian.set_title(0,'Temperature')\n",
    "param_tab = widgets.VBox([BC_accordian,J_accordian,H_accordian,T_accordian,def_but])\n",
    "\n",
    "MCS_accordian = widgets.Accordion(children=[widgets.VBox(MCS_sliders)])\n",
    "MCS_accordian.set_title(0,'Monte-Carlo Steps')\n",
    "Spin_accordian = widgets.Accordion(children=[widgets.GridBox([show_spin],\n",
    "                                                          layout=widgets.Layout(grid_template_columns=\"repeat(1, auto)\"))])\n",
    "Spin_accordian.set_title(0,'Spin')\n",
    "M_accordian = widgets.Accordion(children=[widgets.GridBox([*show_Ms,*show_Mavgs],\n",
    "                                                          layout=widgets.Layout(grid_template_columns=\"repeat(4, auto)\"))])\n",
    "M_accordian.set_title(0,'Magnetization')\n",
    "E_accordian = widgets.Accordion(children=[widgets.GridBox([*show_Es,*show_Eavgs],\n",
    "                                                          layout=widgets.Layout(grid_template_columns=\"repeat(4, auto)\"))])\n",
    "E_accordian.set_title(0,'Energy')\n",
    "measr_tab = widgets.VBox([MCS_accordian,M_accordian,E_accordian,sim_but])\n",
    "\n",
    "tabs = widgets.Tab(children=[init_tab,\n",
    "                             param_tab,\n",
    "                             measr_tab])\n",
    "\n",
    "tabs.set_title(0,\"Initialization\")\n",
    "tabs.set_title(1,\"Parameters\")\n",
    "tabs.set_title(2,\"Measurement\")\n",
    "plot_out = widgets.interactive_output(show_plot, update_dict)\n",
    "out1 = widgets.Output(layout={'border': '0px solid black'})\n",
    "with out1:\n",
    "    out1.clear_output()\n",
    "    display(widgets.VBox([tabs,\n",
    "                          plot_period,\n",
    "                          plot_out,\n",
    "                          status_text,\n",
    "                          widgets.GridBox([init_but,def_but,sim_but], layout=widgets.Layout(grid_template_columns=\"repeat(3, auto)\")),\n",
    "                         ]),\n",
    "                          layout={'color':'black'})\n",
    "out1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "id": "g99vww4lnJC6"
   },
   "outputs": [],
   "source": []
  }
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