Monte-Carlo Methods for the Ising model

Here you can find all of the codes and results used in the paper titled Accurate Estimate of the Joint Density of States via Flat Scan Sampling, arXiv:2203.02718 [cond-mat.stat-mech].

Any questions contact: [email protected]

Suported Models:

• Ising Model
• Ising SpinS Model

Current Methods:

• Wang-Landau
• Flat Scan Sampling

Prerequisits

• C/C++ compiler (compiler has to support the c++17 standard library).

How to use

To use the developed code you have to include system.h and rng.h. Next, depending on the algorithm you want to use, include either fss.h or wl.h. The RNG class takes as input the seed and uses the xoshiro256** algorithm for a fast generation of random numbers. The System class encapsules all of the system's properties and results. It uses as inputs the number unit cells L, the spin degeneracy in the z-direction, the lattice type and finally the relative path to where the normalization, neighbor tables and sum_pos files are stored.

For the FSS method, it can be used like this:

#include <iostream>

#include "../src/system.h"
#include "../src/fss.h"
#include "../src/rng.h"

int main(int argv, char **argc) {
    RNG rng(20);
    System ising_lattice(4, 2, "SS", "../");

    FSS fss(1000, 1, rng, ising_lattice);

    fss.simulate(0, true);
    fss.write_to_file("JDOS.txt", "./", true);
    
    return 0;
}

The FSS class takes as parameters the parameter REP and skip, an instance of the RNG and System classes.

For the WL method, it can be used like this:

#include <iostream>

#include "../src/system.h"
#include "../src/wl.h"
#include "../src/rng.h"

int main(int argv, char **argc) {
    RNG rng(20);
    System ising_lattice(4, 2, "SS");
    
    WL wang_landau(exp(1), 1 + pow(10, -8), 0.9, rng, ising_lattice);
    
    wang_landau.simulate(10000, 0, true);
    wang_landau.print_JDOS();
    
    return 0;
}

The WL class takes as parameters the value of the first and last modification factors, the flatness criteria and an instance of RNG and System.

For spinS computations, it it better to use the MATLAB implementation by J. Amaral [email protected]. A more efficient C++ implementation will come in the near future.