NS_1d_ising_model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3a9a0c2a",
   "metadata": {},
   "source": [
    "# Numerically solving the 1D Ising model with nested sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6233703b",
   "metadata": {},
   "source": [
    "This notebook shows how the thermodynamic behaviour of the 1D Ising model can be numerically determined with nested sampling.\n",
    "\n",
    "The 1d Ising model is made up of a chain of \"spins\", which may point either up or down. In this case we consider N spins with periodic boundary conditions such that the 1st and Nth spins are neighbours, like we have closed the chain at each end to form a loop.\n",
    "\n",
    "A configuration of these spins may for example look like this:\n",
    "\n",
    "\\begin{equation}\n",
    "\\dots \\uparrow \\uparrow \\downarrow \\uparrow \\downarrow \\downarrow \\uparrow \\downarrow \\uparrow\\uparrow \\downarrow \\downarrow\\uparrow\\uparrow \\downarrow \\dots\n",
    "\\end{equation}\n",
    "\n",
    "We represent a configuration with the set of values $\\{\\sigma_i\\}$, where $i$ is the index of each spin ($i = 1,\\dots,N$) and $\\sigma = \\pm 1$\n",
    "\n",
    "Spins interact with their neighbours through exchange coupling, in that each spin may raise or lower the total energy of the system depending on how it aligns with its neighbours.\n",
    "\n",
    "The energy of a configuration is therefore given by the following Hamiltonian:\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{H} = -J \\sum_{\\langle i,j \\rangle} \\sigma_i \\sigma_j\n",
    "\\end{equation}\n",
    "\n",
    "where $J$ is the exchange constant, informing the strength and form of the interactions.\n",
    "\n",
    "If J > 0 spins save energy by aligning, leading to ferromagnetism.\n",
    "\n",
    "If J < 0 spins save energy by anti-aligning, leading to anti-ferromagnetism.\n",
    "\n",
    "$\\langle i,j \\rangle $ indicates that we are summing over nearest neighbour pairs.\n",
    "\n",
    "The order parameter in which we're interested is the total normalised magnetisation, given by:\n",
    "\n",
    "\\begin{equation}\n",
    "   m =  \\frac{1}{N}\\sum_i \\sigma_i\n",
    "\\end{equation}\n",
    "\n",
    "With nested sampling we aim to efficiently sample the different possible configurations and their energies, providing ensemble averages of the energy and total magnetisation at different temperatures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "id": "9248e0be",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\" Nested sampling (NS) of the 1D Ising model \"\"\"\n",
    "\n",
    "import numpy as np\n",
    "import sys\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import trange\n",
    "\n",
    "rng = np.random.default_rng(1)\n",
    "\n",
    "\n",
    "def calculate_energy(configuration):\n",
    "    \"\"\" Calculate the energy of a 1D configuration of spins \"\"\"\n",
    "    energy = 0\n",
    "    for i in range(len(configuration)):\n",
    "        energy -= configuration[i] * configuration[i - 1]\n",
    "    energy += rng.uniform() / 1e6 # add small energy from uniform distribution to lift degeneracies\n",
    "    return energy\n",
    "\n",
    "\n",
    "def find_limit(energies):\n",
    "    \"\"\" Find the index of the maximum-energy walker \"\"\"\n",
    "    energy_limit = np.max(energies)\n",
    "    index_limit = np.argwhere(energies == energy_limit).flatten()\n",
    "    return energy_limit, index_limit\n",
    "\n",
    "def spin_flips(number_of_steps, number_of_spins, energy_limit, walkers, energies, i_limit, verbose=False):\n",
    "    \"\"\" Generation of new walker through cloning and random walk process \"\"\"\n",
    "    \n",
    "    # save data of initial walker \n",
    "    energy_initial = energies[i_limit]\n",
    "    walker_initial = walkers[i_limit]\n",
    "    \n",
    "    # verbosity for bug fixing!\n",
    "    if verbose:\n",
    "        print(f\"INITIAL Walker {i_limit} {walker_initial} Energy {energy_initial} limit {energy_limit}\")\n",
    "    \n",
    "    # choose a walker at random to clone\n",
    "    rand_ind = rng.integers(low=0, high=len(walkers), size=1)[0]\n",
    "    walker = walkers[rand_ind].copy()\n",
    "    \n",
    "    # initial energy of clone\n",
    "    energy_prev = energies[rand_ind].copy()\n",
    "    \n",
    "    if verbose:\n",
    "        energy_check = calculate_energy(walker)\n",
    "        if abs(energy_prev - energy_check) > 0.5:\n",
    "            print(f\"WARNING MISMATCH INIT ENERGY (SAVED: {rand_ind} {energy_prev} RECALC: {energy_check} {walker})\")\n",
    "        #print(\"CLONE:\", rand_ind, energy_prev, walker)\n",
    "        print(f\"CLONE {rand_ind} {walker} Energy {energy_prev}\")\n",
    "    \n",
    "    n_accept = 0\n",
    "    #print(f\"CLONED WALKER: {walker} Energy {energy_prev}\")\n",
    "    for i in range(number_of_steps):\n",
    "\n",
    "        # choose a spin at random\n",
    "        spin = rng.integers(low=0, high=number_of_spins, size=1)[0]\n",
    "        \n",
    "        # flip spin\n",
    "        #print(f\"Step {i} BEFORE Walker {walker}\")\n",
    "        #energy_initial = energy_prev\n",
    "        if verbose:\n",
    "            print(f\"Step {i} BEFORE Walker {walker} Energy {energy_prev}\")\n",
    "        \n",
    "        # flip spin\n",
    "        walker[spin] *= -1\n",
    "        \n",
    "        # check energy after flip\n",
    "        energy = calculate_energy(walker)\n",
    "        \n",
    "        if verbose:\n",
    "            print(f\"Step {i} FLIP {spin} Walker {walker} Energy {energy}\")\n",
    "        \n",
    "        # Does energy exceed the limit set by the initial max energy walker?\n",
    "        # If yes, reject!\n",
    "        if energy >= energy_limit:\n",
    "            if verbose:\n",
    "                print(f\"Step {i} REJECT Walker {walker} energy {energy}  limit {energy_limit}\")\n",
    "            walker[spin] *= -1\n",
    "            energy = energy_prev\n",
    "            if verbose:\n",
    "                print(f\"Step {i} RESTORE Walker {walker} energy {energy}  limit {energy_limit}\")\n",
    "            accept = False\n",
    "        # If no, accept!\n",
    "        else:\n",
    "            n_accept += 1\n",
    "            accept = True\n",
    "            energy_prev = energy\n",
    "            if verbose:\n",
    "                print(f\"Step {i} ACCEPT Walker {walker} energy {energy} limit {energy_limit}\")\n",
    "    \n",
    "    if verbose:\n",
    "        energy_check = calculate_energy(walker)\n",
    "        if abs(energy - energy_check) > 0.5:\n",
    "            print(f\"WARNING MISMATCH AFTER ENERGY (SAVED: {energy} RECALC: {energy_check} {walker})\")\n",
    "        \n",
    "    return walker, energy, n_accept/number_of_steps\n",
    "\n",
    "def run_ns(N_spin = 50, N_walker = 200, N_iteration = 50000, N_step = 100, N_record = 100):\n",
    "    \"\"\" \"\"\"\n",
    "    # Parameters for NS of the 1D Ising model\n",
    "    # N_spin = number of spins in 1D Ising model\n",
    "    # N_walker = number of walkers in NS\n",
    "    # N_iteration = number of iterations in NS\n",
    "    # N_step = number of steps per walk\n",
    "    # N_record = frequency at which configurations are saved\n",
    "    \n",
    "    # Generate `N_walker` walkers (W) each with `N_spin` spins\n",
    "    W = rng.integers(low=0, high=2, size=(N_walker, N_spin)) * 2 - 1\n",
    "    E_W = np.apply_along_axis(calculate_energy, 1, W)  # energies (E) of walkers\n",
    "\n",
    "    # Start NS\n",
    "    E_limit = np.zeros(N_iteration)\n",
    "    mag_limit = np.zeros(N_iteration)\n",
    "    saved_configs = []\n",
    "    \n",
    "    for i in trange(N_iteration):\n",
    "        # Find maximum-energy walker and store its energy and magnetisation\n",
    "        E_limit_i, i_limit = find_limit(E_W)\n",
    "        E_limit[i] = E_limit_i\n",
    "        mag_limit[i] = np.sum(W[i_limit[0]])\n",
    "        \n",
    "        # Store configuration after N_record iterations\n",
    "        if i%N_record == 0:\n",
    "            config_info = {\n",
    "                \"configuration\": W[i_limit[0]].copy(),\n",
    "                \"iteration\": i+1,\n",
    "                \"energy\": E_limit_i,\n",
    "                \"magnetisation\": mag_limit[i],\n",
    "                \"temperature\": None\n",
    "            }\n",
    "            saved_configs += [config_info]\n",
    "\n",
    "        # Generate walker to replace maximum-energy walker\n",
    "        if False: #i%1000 == 0:\n",
    "            verbose = True\n",
    "        else:\n",
    "            verbose = False\n",
    "                \n",
    "        W_i, E_W_i, acc_ratio = spin_flips(N_step, N_spin, E_limit_i, W, E_W, i_limit[0], verbose=verbose)\n",
    "\n",
    "        # Replace maximum energy walker with cloned and decorrelated walker\n",
    "        W[i_limit[0]] = W_i.copy()\n",
    "        E_W[i_limit[0]] = E_W_i.copy()\n",
    "    \n",
    "    return E_limit, mag_limit, saved_configs\n",
    "\n",
    "def analyse_NS(energies, magnetisations, N_walker, N_spin, kTdiv=0.05, kTmax=4):\n",
    "    \"\"\" Calculate ensemble averages of energy, magnetisation and absolute magnetisation over range of temperatures \"\"\" \n",
    "    \n",
    "    chi_0 = 1E7 #arbitrary scaling factor\n",
    "    \n",
    "    #list of iteration numbers\n",
    "    iters = np.arange(len(energies)) + 1\n",
    "    \n",
    "    # Phase space volume below configuration of iteration i-1\n",
    "    zetas_old = (N_walker / (N_walker + 1)) ** (iters - 1)\n",
    "    # Phase space volume below configuration of iteration i\n",
    "    zetas_new = (N_walker / (N_walker + 1)) ** iters\n",
    "    delta_chi = chi_0 * (zetas_old - zetas_new)\n",
    "    \n",
    "    #list of temperatures at which average quantities are calculated\n",
    "    kTs = np.linspace(kTdiv, kTmax, int(kTmax / kTdiv))\n",
    "    \n",
    "    #empty lists of average energies, magnetisations\n",
    "    enavg_energ = np.zeros(len(kTs))\n",
    "    enavg_mag = np.zeros(len(kTs))\n",
    "    enavg_absmag = np.zeros(len(kTs))\n",
    "    \n",
    "    #reference energy\n",
    "    E0 = min(energies)\n",
    "    \n",
    "    #sum for calculation of ensemble averages\n",
    "    for i, kT in enumerate(kTs):\n",
    "        eng_numer = np.sum(delta_chi * np.exp(-(energies-E0) / kT) * energies)\n",
    "        mag_numer = np.sum(delta_chi * np.exp(-(energies-E0) / kT) * magnetisations)\n",
    "        absmag_numer = np.sum(delta_chi * np.exp(-(energies-E0) / kT) * np.absolute(magnetisations))\n",
    "        denom = np.sum(delta_chi * np.exp(-(energies-E0) / kT))\n",
    "        enavg_energ[i] = eng_numer / denom / N_spin\n",
    "        enavg_mag[i] = mag_numer / denom / N_spin\n",
    "        enavg_absmag[i] = absmag_numer / denom / N_spin\n",
    "        \n",
    "    return kTs, enavg_energ, enavg_mag, enavg_absmag\n",
    "\n",
    "def multi_run(N_run = 3, N_spin = 50, N_walker = 200, N_iteration = 50000, N_step = 100, N_record = 100):\n",
    "    \"\"\" Perform multiple runs of NS with the same hyperparameters, to assess convergence.\"\"\"\n",
    "    energies_list = []\n",
    "    mags_list = []\n",
    "    configs_list = []\n",
    "    for i in range(N_run):\n",
    "        print(f\"Performing NS run {i+1}...\")\n",
    "        energies, magnetisations, configurations = run_ns(N_spin=N_spin, N_walker=N_walker, \n",
    "                                                          N_iteration=N_iteration, N_step=N_step)\n",
    "        \n",
    "        energies_list += [energies]\n",
    "        mags_list += [magnetisations]\n",
    "        configs_list += [configurations]\n",
    "        \n",
    "    return energies_list, mags_list, configs_list\n",
    "                \n",
    "def multi_analyse(energies_list, mags_list, N_walker, N_spin, kTdiv=0.05, kTmax=4):\n",
    "    \"\"\" Calculate ensemble averages for multiple NS runs and plot the results. \"\"\"\n",
    "    enavg_eng_list = []\n",
    "    enavg_mag_list = []\n",
    "    enavg_absmag_list = []\n",
    "    \n",
    "    plt.xlabel(\"$k_B T / J$\")\n",
    "    \n",
    "    for i in range(len(energies_list)):\n",
    "        kTs, enavg_energ, enavg_mag, enavg_absmag = analyse_NS(energies_list[i], mags_list[i], \n",
    "                                                               N_walker=N_walker, N_spin=N_spin,\n",
    "                                                               kTdiv=kTdiv, kTmax=kTmax)\n",
    "                \n",
    "        enavg_eng_list += [enavg_energ]\n",
    "        enavg_mag_list += [enavg_mag]\n",
    "        enavg_absmag_list += [enavg_absmag]\n",
    "        plt.figure(0)\n",
    "        plt.plot(kTs, enavg_energ, \"--\", label=f\"NS run {i+1}\")\n",
    "        plt.figure(1)\n",
    "        plt.plot(kTs, enavg_absmag, \"--\", label=f\"NS run {i+1}\")\n",
    "        plt.figure(2)\n",
    "        plt.plot(kTs, enavg_mag, \"--\", label=f\"NS run {i+1}\")\n",
    "    \n",
    "    plt.figure(0)\n",
    "    plt.title(f\"1D Ising Model with {N_spin} Spins, using {N_walker} walkers, {N_iteration} iterations, {N_step} steps per iter.\")\n",
    "    exact_E = -np.tanh(1 / kTs)\n",
    "    plt.xlabel(\"$k_B T / J$\")\n",
    "    plt.ylabel(r\"Free energy\")\n",
    "    plt.plot(kTs, exact_E, \"black\", label=\"Exact\")\n",
    "    plt.legend()\n",
    "    plt.plot()\n",
    "    \n",
    "    plt.figure(1)\n",
    "    plt.title(f\"1D Ising Model with {N_spin} Spins, using {N_walker} walkers, {N_iteration} iterations, {N_step} steps per iter.\")\n",
    "    plt.xlabel(\"$k_B T / J$\")\n",
    "    plt.ylabel(r\"Absolute magnetisation $\\langle m \\rangle$\")\n",
    "    #plt.plot(kTs, exact_E, \"black\", label=\"Exact\")\n",
    "    plt.legend()\n",
    "    \n",
    "    plt.figure(2)\n",
    "    plt.title(f\"1D Ising Model with {N_spin} Spins, using {N_walker} walkers, {N_iteration} iterations, {N_step} steps per iter.\")\n",
    "    plt.xlabel(\"$k_B T / J$\")\n",
    "    plt.ylabel(r\"Magnetisation $\\langle | m | \\rangle$\")\n",
    "    #plt.plot(kTs, exact_mag, \"black\", label=\"Exact\")\n",
    "    plt.legend()\n",
    "\n",
    "def plot_ensemble_average_energy(kTs, enavg_energ, N_walker, N_spin, N_iteration, N_step):\n",
    "    \"\"\" Plot ensemble averages of energy (free energy) for results of single run. \"\"\"\n",
    "    \n",
    "    plt.plot(kTs, enavg_energ, \"C0--\", label=\"Nested sampling\")\n",
    "    # Exact result for free energy\n",
    "    exact_E = -np.tanh(1 / kTs)\n",
    "    plt.plot(kTs, exact_E, \"C0\", label=\"Exact\")\n",
    "    plt.xlabel(\"$k_B T / J$\")\n",
    "    plt.ylabel(r\"$\\langle E \\rangle / N J$\")\n",
    "    plt.title(f\"1D Ising Model with {N_spin} Spins, using {N_walker} walkers, {N_iteration} iterations, {N_step} steps per iter.\")\n",
    "    plt.legend()\n",
    "    \n",
    "def plot_ensemble_average_mag(kTs, enavg_mag, N_walker, N_spin, N_iteration, N_step):\n",
    "    \"\"\" Plot ensemble averages of magnetisation for results of single run. \"\"\"\n",
    "    \n",
    "    plt.plot(kTs, enavg_mag, \"C0--\", label=\"Nested sampling\")\n",
    "    plt.xlabel(\"$k_B T / J$\")\n",
    "    plt.ylabel(r\"$\\langle E \\rangle / N J$\")\n",
    "    plt.title(f\"1D Ising Model with {N_spin} Spins, using {N_walker} walkers, {N_iteration} iterations, {N_step} steps per iter.\")\n",
    "    plt.legend()\n",
    "    \n",
    "def plot_ensemble_average_absmag(kTs, enavg_absmag, N_walker, N_spin, N_iteration, N_step):\n",
    "    \"\"\" PLot ensemble averages of absolute magnetisation for results of single run. \"\"\"\n",
    "    \n",
    "    plt.plot(kTs, enavg_absmag, \"C0--\", label=\"Nested sampling\")\n",
    "    plt.xlabel(\"$k_B T / J$\")\n",
    "    plt.ylabel(r\"$\\langle E \\rangle / N J$\")\n",
    "    plt.title(f\"1D Ising Model with {N_spin} Spins, using {N_walker} walkers, {N_iteration} iterations, {N_step} steps per iter.\")\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbd86035",
   "metadata": {},
   "source": [
    "The following commands will run NS using a given set of hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "id": "df8296f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performing NS run 1...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████| 65/65 [00:00<00:00, 2134.32it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performing NS run 2...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████| 65/65 [00:00<00:00, 1863.87it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performing NS run 3...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████| 65/65 [00:00<00:00, 2004.65it/s]\n"
     ]
    }
   ],
   "source": [
    "# Parameters for NS of the 1D Ising model\n",
    "N_spin = 5  # number of spins in 1D Ising model\n",
    "N_walker = 20  # number of walkers in NS\n",
    "N_iteration = 65 # number of iterations in NS\n",
    "N_step = 20 # number of steps per walk\n",
    "\n",
    "N_run = 3 # number of independent NS runs\n",
    "\n",
    "energies_list, mags_list, configs_list = multi_run(N_run=N_run, N_spin=N_spin, N_walker=N_walker, \n",
    "                                                   N_iteration=N_iteration, N_step=N_step)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a3644ab",
   "metadata": {},
   "source": [
    "With the following command we can analyse the output of NS and plot ensemble averages as a function of temperature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "id": "d26cd87a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# These parameters set the range of temperatures over which ensemble averages will be calculated\n",
    "kTdiv = 0.05 # temperature difference\n",
    "kTmax = 4 # maximum temperature\n",
    "\n",
    "multi_analyse(energies_list, mags_list, N_walker=N_walker, N_spin=N_spin, kTdiv=kTdiv, kTmax=kTmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "277cbe0a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}