Monte Carlo study of the random-field Ising model

TL;DR

This study employs advanced Monte Carlo techniques to analyze the three-dimensional random-field Ising model, accurately determining critical parameters and overcoming previous simulation challenges.

Contribution

It introduces a cluster-flipping Monte Carlo algorithm combined with histogram reweighting to efficiently study the equilibrium properties of the 3D random-field Ising model.

Findings

Critical exponents: nu=1.02, beta=0.06, gamma=1.9, gammabar=2.9

System sizes up to 32x32x32 were simulated

The method overcomes slow equilibration in single-spin-flip algorithms

Abstract

Using a cluster-flipping Monte Carlo algorithm combined with a generalization of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied the equilibrium properties of the thermal random-field Ising model on a cubic lattice in three dimensions. We have equilibrated systems of LxLxL spins, with values of L up to 32, and for these systems the cluster-flipping method appears to a large extent to overcome the slow equilibration seen in single-spin-flip methods. From the results of our simulations we have extracted values for the critical exponents and the critical temperature and randomness of the model by finite size scaling. For the exponents we find nu = 1.02 +/- 0.06, beta = 0.06 +/- 0.07, gamma = 1.9 +/- 0.2, and gammabar = 2.9 +/- 0.2.