A new comprehensive study of the 3D random-field Ising model via sampling the density of states in dominant energy subspaces

TL;DR

This study employs a novel numerical approach combining Wang-Landau sampling and broad histogram methods to analyze the 3D bimodal random-field Ising model, focusing on finite-size scaling and non-self-averaging effects.

Contribution

It introduces a unified algorithm using the N-fold Wang-Landau method in dominant energy subspaces for the first time applied to this model.

Findings

Scaling behavior of the model is characterized.

Finite-size anomalies are analyzed with respect to non-self-averaging.

Probability distributions of specific heat and susceptibility are examined.

Abstract

The three-dimensional bimodal random-field Ising model is studied via a new finite temperature numerical approach. The methods of Wang-Landau sampling and broad histogram are implemented in a unified algorithm by using the N-fold version of the Wang-Landau algorithm. The simulations are performed in dominant energy subspaces, determined by the recently developed critical minimum energy subspace technique. The random fields are obtained from a bimodal distribution, that is we consider the discrete $(\pm\Delta)$ case and the model is studied on cubic lattices with sizes $4\leq L \leq 20$. In order to extract information for the relevant probability distributions of the specific heat and susceptibility peaks, large samples of random field realizations are generated. The general aspects of the model's scaling behavior are discussed and the process of averaging finite-size anomalies in random systems is re-examined under the prism of the lack of self-averaging of the specific heat and susceptibility of the model.