Thermal critical behavior and universality aspects of the three-dimensional random-field Ising model

TL;DR

This study investigates the critical behavior and universality of the three-dimensional random-field Ising model using advanced simulation techniques, revealing the influence of disorder strength on self-averaging and phase transition properties.

Contribution

It applies the Wang-Landau algorithm with critical minimum energy subspace technique to analyze the model's phase diagram and specific heat behavior across various disorder strengths.

Findings

Specific heat saturation is re-examined.

Universality is strongly affected by lack of self-averaging.

Disorder strength influences finite-size and critical behavior.

Abstract

The three-dimensional bimodal random-field Ising model is investigated using the N-fold version of the Wang-Landau algorithm. The essential energy subspaces are determined by the recently developed critical minimum energy subspace technique, and two implementations of this scheme are utilized. The random fields are obtained from a bimodal discrete $(\pm\Delta)$ distribution, and we study the model for various values of the disorder strength $\Delta$, $\Delta=0.5, 1, 1.5$ and 2, on cubic lattices with linear sizes $L=4-24$. We extract information for the probability distributions of the specific heat peaks over samples of random fields. This permits us to obtain the phase diagram and present the finite-size behavior of the specific heat. The question of saturation of the specific heat is re-examined and it is shown that the open problem of universality for the random-field Ising model is strongly influenced by the lack of self-averaging of the model. This property appears to be substantially depended on the disorder strength.