Skip to content

ADD: 2D Ising example #69

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
noDGodiaev wants to merge 1 commit into
base: master
Choose a base branch
from
Open

ADD: 2D Ising example #69

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
344 changes: 344 additions & 0 deletions examples/2D-Ising.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,344 @@
{
"cells": [
{
"cell_type": "markdown",
"source": [],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"### Simulation a 2 dimensional Ising model on square lattice with or without frustrations\n",
"The simulation is a single spin flip Monte Carlo Metropolis algorithm.\n",
"To start the simulation call IsingSimulate() function\n",
"\n",
"MCM steps - Monte Carlo Metropolis steps\n",
"```\n",
"IsingSimulate() function\n",
"parameters:\n",
" L - linear lattice size\n",
" T - temperature value\n",
" sweeps - number of MCM steps\n",
" T_corr - number of MCM steps between configuration records in the output array\n",
" J - value of spins neigbours interaction\n",
" Jd - value of diagonal spins neigbours interaction\n",
" seed - seed for mc_lib rndm initialisation\n",
" rseed - seedSequence for mc_lib rndm initialisation\n",
"\n",
"outputs:\n",
" configs\n",
" e - mean energy for the whole simulation\n",
" m - mean magnetisation\n",
"```\n",
"Example [https://colab.research.google.com/drive/1Xwsx39wkBaopYTNswiy2OenMIx5lYBLZ?usp=sharing](https://colab.research.google.com/drive/1Xwsx39wkBaopYTNswiy2OenMIx5lYBLZ?usp=sharing)\n"
],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"outputs": [],
"source": [
"# Check if mc_lib installed\n",
"try:\n",
" from mc_lib.rndm import RndmWrapper\n",
"except ImportError:\n",
" !pip install git+https://github.com/ev-br/mc_lib.git@master\n",
" pass"
],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%%\n"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"outputs": [],
"source": [
"%load_ext cython"
],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%%\n"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"outputs": [],
"source": [
"%%cython --cplus\n",
"import cython\n",
"import numpy as np\n",
"cimport numpy as np\n",
"from libc.math cimport exp\n",
"from mc_lib.rndm cimport RndmWrapper\n",
"from mc_lib.lattices import tabulate_neighbors\n",
"from mc_lib.observable cimport RealObservable\n",
"\n",
"@cython.boundscheck(False) # turn off bounds-checking for entire function\n",
"@cython.wraparound(False) # turn off negative index wrapping for entire function\n",
"cdef np.ndarray initState(long[::1] lattice,\n",
" RndmWrapper rndm):\n",
"\"\"\"\n",
"\n",
":param lattice: unconfigured array of future lattice (empty array)\n",
":param rndm: class with random methods from mc_lib\n",
":return: change the 'Lattice' variable and return nothing\n",
"\"\"\"\n",
"for i in range(lattice.shape[0]):\n",
" lattice[i] = 1 if rndm.uniform() > 0.5 else -1\n",
"return\n",
"\n",
"\n",
"@cython.boundscheck(False)\n",
"@cython.wraparound(False)\n",
"cdef np.ndarray mcmove(long[::1] config,\n",
" double beta,\n",
" long[:, ::1] ngb,\n",
" RndmWrapper rndm,\n",
" const double[:,::1] Js):\n",
"\"\"\"\n",
"One flip attempt\n",
":param config: Current configuration of lattice\n",
":param beta: Inversed temperature of current configuration\n",
":param L: Linear size 'L' of lattice\n",
":param ngb: Array of neigbours\n",
"\"\"\"\n",
"cdef:\n",
"Py_ssize_t site = int(config.shape[0] * rndm.uniform())\n",
"Py_ssize_t site1 = 0\n",
"double dE = 0\n",
"long num_ngb = ngb[site, 0]\n",
"for n in range(1, num_ngb + 1):\n",
" site1 = ngb[site, n]\n",
" dE += config[site1] * config[site] * Js[site,site1]\n",
"cdef double ratio = exp(-2 * dE * beta)\n",
"if rndm.uniform() > ratio:\n",
" return\n",
"config[site] *= -1\n",
"return\n",
"\n",
"\n",
"@cython.boundscheck(False)\n",
"@cython.wraparound(False)\n",
"cdef double calcEnergy(long[::1] config,\n",
" long[:, ::1] ngb,\n",
" const double[:,::1] Js):\n",
"\"\"\"\n",
" Count current configuration energy\n",
" :param config: Current configuration of lattice\n",
" :param ngb: Array of neigbours\n",
" return:\n",
"\"\"\"\n",
"cdef:\n",
"Py_ssize_t site = 0\n",
"Py_ssize_t site1 = 0\n",
"double energy = 0\n",
"for site in range(config.shape[0]):\n",
" num_ngb = ngb[site, 0]\n",
" for n in range(1, num_ngb+1):\n",
" site1 = ngb[site, n]\n",
" energy += -1 * config[site] * config[site1] * Js[site, site1]\n",
"return energy / 4.\n",
"\n",
"\n",
"def get_J( double[:,::1] Js, double J, double Jd, int L1, int L2):\n",
"\"\"\"Tabulate the couplings per site.\"\"\"\n",
"cdef Py_ssize_t i\n",
"for i in range(L1*L2):\n",
" Js[i, ((i // L2 + 1) % L1 * L2 ) + (i + 1) % L2 ] = Jd\n",
" Js[i, ((i // L2 - 1) % L1 * L2 ) + (i - 1) % L2 ] = Jd\n",
" Js[i, (i // L2) * L2 + (i + 1) % L2] = J\n",
" Js[i, (i + L2) % (L1*L2)] = J\n",
" Js[i, (i // L2) * L2 + (i - 1) % L2] = J\n",
" Js[i, (i - L2) % (L1*L2)] = J\n",
"return\n",
"\n",
"\n",
"@cython.boundscheck(False)\n",
"@cython.wraparound(False)\n",
"def IsingSimulate(L, T, sweeps, int T_corr, double J=1, double Jd=0, int seed = np.random.randint(0, 1000), int rseed = 1234):\n",
"\"\"\"\n",
" L - linear_size\n",
" T - One temperature point\n",
" J - value of spins neigbours interaction\n",
" Jd - value of diagonal spins neigbours interaction\n",
" Sweeps - number of L^2 Metropolis Monte-Karlo steps\n",
"\"\"\"\n",
"cdef RndmWrapper rndm = RndmWrapper((rseed, seed))\n",
"cdef:\n",
"float beta = 1.0 / T\n",
"int sweep = 0\n",
"int steps_per_sweep = L * L\n",
"int num_therm = int(12 * L * L)\n",
"int i = 0\n",
"\n",
"cdef:\n",
"np.ndarray configs = np.empty([sweeps, L*L], dtype=int)\n",
"long[::1] config = np.empty(L*L, dtype=int)\n",
"int steps = 0\n",
"long[:, ::1] ngb\n",
"if Jd == 0:\n",
" ngb = tabulate_neighbors((L, L, 1), kind='sc')\n",
"else:\n",
" ngb = tabulate_neighbors(L, kind='triang')\n",
"\n",
"cdef double[:,::1] Js = np.zeros((L*L, L*L))\n",
"get_J(Js, J, Jd, L, L)\n",
"\n",
"cdef RealObservable m1 = RealObservable()\n",
"cdef RealObservable e1 = RealObservable()\n",
"\n",
"initState(config, rndm)\n",
"for sweep in range(num_therm):\n",
" mcmove(config, beta, ngb, rndm, Js)\n",
"\n",
"\n",
"for sweep in range(sweeps):\n",
" for i in range(T_corr):\n",
" steps += 1\n",
" for i in range(steps_per_sweep):\n",
" mcmove(config, beta, ngb, rndm, Js)\n",
" configs[sweep] = config.copy()\n",
" energ = calcEnergy(config, ngb, Js)\n",
" magn = np.sum(config)\n",
" e1.add_measurement(energ)\n",
" m1.add_measurement(magn)\n",
"\n",
"return configs, e1.mean, m1.mean"
],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%%\n"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"outputs": [],
"source": [
"IsingSimulate(L=4, T=2.26, sweeps=100, T_corr=1, J=1, Jd=0, seed=10, rseed=10)"
],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%%\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"## Energy and magnetisation graphs"
],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"outputs": [],
"source": [
"%%time\n",
"import numpy as np\n",
"ms = []\n",
"es = []\n",
"configs = []\n",
"L = 20\n",
"Temps = np.linspace(1.8, 3, 30)\n",
"for i, t in enumerate(Temps):\n",
" config, e, m = IsingSimulate(L=L, T=t, sweeps=10000, T_corr=50, J=1, Jd=0, seed=0)\n",
" es.append(e)\n",
" ms.append(m)\n",
" configs.append(config)\n",
" if i%10 == 0:\n",
" print(t)\n",
"es = np.array(es)\n",
"ms = np.array(ms)\n",
"configs = np.array(configs)"
],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%%\n"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"outputs": [],
"source": [
"try:\n",
" import matplotlib.pyplot as plt\n",
" fig = plt.figure(figsize=(7, 5))\n",
" fontsize = 16\n",
" T_c = 2 / (np.log(1 + 2 ** 0.5))\n",
" plt.scatter(Temps, es / L**2, marker = \"o\", linestyle=\"None\", label='E(T)')\n",
" plt.axvline(T_c, color=\"tab:orange\")\n",
" plt.legend(fontsize=fontsize)\n",
" plt.xlabel(\"T\", fontsize=fontsize)\n",
" plt.ylabel(r\"E(t) / $L^2$\", fontsize=fontsize)\n",
" plt.grid()\n",
" fig = plt.figure(figsize=(7, 5))\n",
" plt.scatter(Temps, np.abs(ms / L**2), marker = \"o\", linestyle=\"None\", label='M(T)')\n",
" plt.axvline(T_c, color=\"tab:orange\")\n",
" plt.legend(fontsize=fontsize)\n",
" plt.xlabel(\"T\", fontsize=fontsize)\n",
" plt.ylabel(r\"M(t) / $L^2$\", fontsize=fontsize)\n",
" plt.grid()\n",
"except ImportError:\n",
" print('You need matplotlib be installed')\n"
],
"metadata": {
"collapsed": false,
"pycharm": {
"name": "#%%\n"
}
}
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}