Spinner: a spin system simulation library

This is Spinner, a collection of numerical routines for spin systems simulations. Spinner is free software, you can redistribute it and/or modify it under the terms of the GNU General Public License.

WARNING: This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

NOTE: This library is in early stage of development. Contributions are welcome.

Introduction

Spin systems, such as the Ising or the Heisenberg model, are defined on a graph where each vertex $i$ has a (symmetric) interaction $J_{ij}$ with its neighbors $j$. This library allows the creation of a graph object that is used by one or more system objects. You can then apply a stepper object to move the system in its configuration space using a Monte Carlo Markov Chain (MCMC) method.

The system object can hold spin variables of different kinds, such as Ising variables ($s_i=\pm1$), or n-vector variables ($\mathbf{s}i\in\mathbb{R}^n:|s_i|=1$). The graph kind holds the coupling constants $J{ij}$ that make up the graph. Graph structures can be of the following kinds:

Read the documentation for a detailed explanation.

Building and using

Here are the building instructions:

git clone <spinner repo>
cd spinner
autoreconf -i
./configure
make
sudo make install

The default installation prefix is /usr/local/lib.

Usage example

Here is an example code that, at different temperatures, samples:

• an Ising system
• on a cubic lattice in 2D with side 50 (N=2500 sites)
• with ferromagnetic interactions
• every 10*N steps using the Metropolis algorithm

#include <stdio.h>
#include <spinner/spinner.h>

int main()
{
  size_t N = 2500, n_temps = 50, n_probes = 1000+1, i;
  float temp, temp_start = 0.1, temp_finish=5.0, temp_step, beta;
  float h_mean, m_mean, h_var, m_var;
  FILE * f;
  
  spnr_graph_t *graph = spnr_graph_alloc (spnr_cubic, spnr_ferr, N, 2);
  spnr_sys_t *sys = spnr_sys_alloc (graph, spnr_ising, 2);
  spnr_step_t *step = spnr_step_alloc (spnr_metropolis,
                                       spnr_sys_spin_size(sys));
  spnr_data_t *data = spnr_data_alloc (n_probes);
  
  temp_step = (temp_finish - temp_start) / (float) (n_temps-1);
  f = fopen ("results.txt", "w");
  for (i = 0; i < n_temps; ++i)
    {
      temp = temp_start + i * temp_step;
      beta = 1.0 / temp;
      
      spnr_data_run_and_probe (data, sys, step, temp, 10);
      spnr_data_mean_calc (data, &h_mean, &m_mean);
      spnr_data_var_calc (data, &h_var, &m_var);
      fprintf (f, "%f %+f %+f %+f %+f\n", temp, h_mean, m_mean,
               beta * beta * N * h_var, beta * N * m_var);
    }
  fclose (f);
  
  spnr_data_free (data);
  spnr_step_free (step);
  spnr_sys_free (sys);
  spnr_graph_free (graph);
}

To compile:

gcc -I /usr/local/include/ program.c -o program -L /usr/local/lib -lspinner -lm

Upon execution, it will produce a file. Using gnuplot with the following command

plot "results.txt" using 1:4 with lines

yelds

Planned features:

Here are the planned features for this library. For now, only some of them are in place.

• Variables
  • Ising
  • n-vector (XY, Heisenberg)
  • Potts
• Graphs
  • Cubic lattice
  • Fully connected
  • Random graph
• Interactions
  • Ferromagnetic
  • Antiferromagnetic
  • Spin glass (bimodal)
• Steppers
  • Metropolis
  • Heat-Bath
  • Wolff
  • Swendsen–Wang
• Utilities
  • Simulation data object
  • Parallelization
  • Parallel tempering