OpenJij/OpenJij

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docs/tutorial/en/physics/MonteCarloSampling.ipynb

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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Monte Carlo Sampling and Estimation of Phase Transition Point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OpenJij performs simulated annealing (SA).\n",
    "If the temperature is constant, spins can be sampled from the canonical ensemble of that temperature.\n",
    "The canonical ensemble is:\n",
    "\n",
    "$$\n",
    "p(\\{\\sigma\\}) = \\frac{\\exp(-\\beta E(\\{\\sigma\\}))}{Z}, \\ Z = \\sum_{\\{\\sigma\\}}\\exp(-\\beta E(\\{\\sigma\\}))\n",
    "$$\n",
    "\n",
    "In the following, we use a fully-connected ferromagnetic Ising model:\n",
    "\n",
    "$$\n",
    "E(\\{\\sigma\\}) = \\frac{J}{N} \\sum_{i<j} \\sigma_i \\sigma_j \\ (J<0)\n",
    "$$\n",
    "\n",
    "We normalize the Hamiltonian by dividing the energy by the system size $N$.\n",
    "Also, we set $J = -1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import library\n",
    "import openjij as oj\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# set sampler\n",
    "sampler = oj.SASampler(num_reads=100)\n",
    "\n",
    "# define the fully-connected problem\n",
    "def fully_connected(n):\n",
    "    h, J = {}, {}\n",
    "    for i in range(n-1):\n",
    "        for j in range(i+1, n):\n",
    "            J[i, j] = -1/n\n",
    "    return h, J\n",
    "\n",
    "# set h and J\n",
    "h, J = fully_connected(n=500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us calculate the magnetization at each temperature.\n",
    "\n",
    "$$\n",
    "m = \\frac{1}{N} \\sum_i \\sigma_i\n",
    "$$\n",
    "\n",
    "If the magnetization is closer to 1, the state is in the ordered state (ferromagnetic). Conversely, if it is closer to 0, the state is in the disordered state (paramagnetic).\n",
    "When the temperature is kept constant, it can be seen that the magnetization approaches 0 at a temperature of around 1.0.\n",
    "This is because the phase transition theoretically occurs in the infinite size limit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a list of temperatures\n",
    "temp_list = np.linspace(0.01, 2, 30)\n",
    "\n",
    "# calculate the magnetization and its dispersion\n",
    "mag, mag_std = [], []\n",
    "for temp in temp_list:\n",
    "    beta = 1.0/temp\n",
    "    schedule = [[beta, 100]]\n",
    "    response = sampler.sample_ising(h, J, schedule=schedule)\n",
    "    mag_list = [np.abs(np.mean(state)) for state in response.states]\n",
    "    mag_std.append(np.std(mag_list))\n",
    "    mag.append(np.mean(mag_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plt.errorbar(temp_list, mag, yerr=mag_std)\n",
    "plt.plot(temp_list, mag)\n",
    "plt.xlabel('temperature', fontsize=15)\n",
    "plt.ylabel(r'$|m|$', fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Phase transition** is the phenomenon that changes the value significantly at a specific temperature.\n",
    "In the present model, it is theoretically proven that a phase transition occurs at a temperature of 1.0 in the thermodynamic limit.  \n",
    "However, in many cases, it is difficult to study the properties of the phase transition analytically. For this reason, many methods use Monte Carlo simulations to study the properties of the phase transitions numerically."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binder Cumulant\n",
    "\n",
    "Let us assume that we do not know the phase transition temperature, and let us try to find it as accurately as possible from numerical calculations.\n",
    "The above figure shows that the magnetization is approaching zero as the temperature increases.\n",
    "However, it needs to be made clear which temperature is the phase transition point.\n",
    "This is because the phase transition phenomenon theoretically occurs in a system of infinite size, but the simulation can only handle a finite size, resulting in an error with the theory. This is called the **finite-size effect**.  \n",
    "It may seem impossible to numerically analyze a system of infinite size.\n",
    "However, in the field of numerical statistical mechanics, methods have been developed to obtain information on the infinite size limit from finite system sizes.\n",
    "One of these methods uses the **Binder cumulant**.\n",
    "Binder cumulant is:\n",
    "\n",
    "$$U_4 \\equiv \\frac{1}{2}\\left( 3- \\frac{\\langle m^4\\rangle}{\\langle m^2\\rangle^2} \\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate U_4\n",
    "def u_4(states):\n",
    "    m = np.array([np.mean(state) for state in states])\n",
    "    return 0.5 * (3-np.mean(m**4)/(np.mean(m**2)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can show that this quantity approaches 1 for ferromagnetic state, where the magnetization approaches 1, and 0 for paramagnetic state, where the magnetization approaches 0.\n",
    "Furthermore, it is known that the value is independent of system size at the phase transition point.\n",
    "Therefore, numerical experiments can be performed for several system sizes, and the phase transition point is the point where $U_4$ for several system sizes intersect.\n",
    "Please check statistical mechanics textbooks for more information.\n",
    "Let us perform the calculation with OpenJij."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the size of the system as a list\n",
    "n_list = [40, 80, 120, 160]\n",
    "# Define temperature by list\n",
    "temp_list = np.linspace(0.5, 1.5, 30)\n",
    "\n",
    "# Set sampler\n",
    "sampler = oj.SASampler(num_reads=300)\n",
    "\n",
    "u4_list_n = []\n",
    "for n in n_list:\n",
    "    # Create instance\n",
    "    h, J = fully_connected(n)\n",
    "    u4_temp = []\n",
    "    for temp in temp_list:\n",
    "        beta = 1.0/temp\n",
    "        schedule = [[beta, 100 if temp < 0.9 else 300]]\n",
    "        response = sampler.sample_ising(h, J, \n",
    "                                        schedule=schedule, reinitialize_state=False,\n",
    "                                        num_reads=100 if temp < 0.9 else 1000\n",
    "                                       )\n",
    "        u4_temp.append(u_4(response.states))\n",
    "    u4_list_n.append(u4_temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "for n,u4_beta in zip(n_list,u4_list_n):\n",
    "    plt.plot(temp_list, np.array(u4_beta), label='n={}'.format(n))\n",
    "\n",
    "plt.legend()\n",
    "plt.ylabel('$U_4$', fontsize=15)\n",
    "plt.xlabel('temperature', fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The statistics are not enough, so the data is a little scattered.\n",
    "However, it can be seen that the data for the four system sizes intersect at a single point around the temperature of 1, which is approximately the phase transition point.  \n",
    "Estimation of the phase transition point by Binder cumulant is a common method used in numerical analysis.\n",
    "\n",
    "> In academic research, it is necessary to obtain sufficient statistics, and of course, error evaluation (calculation of error bars) must be done more precisely.\n",
    "Since the present calculations are only an overview, the exact error evaluations are omitted."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "We have shown how to perform Monte Carlo sampling using OpenJij.\n",
    "We applied it to an estimation of phase transitions point.\n",
    "OpenJij can be used for various applications depending on your ideas."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.15"
  },
  "vscode": {
   "interpreter": {
    "hash": "2e8d7574d7ec71e14cb1575cf43673432d6fae464c836a7b3733d4f6c20243fb"
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  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}