Wang-Landau study of the 3D Ising model with bond disorder

TL;DR

This study uses an advanced Wang-Landau algorithm to analyze the critical behavior of the 3D Ising model with bond disorder, revealing it shares a universality class with other disordered variants.

Contribution

It introduces a two-stage Wang-Landau approach to study the 3D disordered Ising model and establishes its universality class with other disordered models.

Findings

Disordered 3D Ising model shares universality class with site- and bond-diluted models.

Critical exponents indicate a continuous phase transition.

Finite-size scaling confirms the universality class across different disorder types.

Abstract

We implement a two-stage approach of the Wang-Landau algorithm to investigate the critical properties of the 3D Ising model with quenched bond randomness. In particular, we consider the case where disorder couples to the nearest-neighbor ferromagnetic interaction, in terms of a bimodal distribution of strong versus weak bonds. Our simulations are carried out for large ensembles of disorder realizations and lattices with linear sizes $L$ in the range $L=8-64$. We apply well-established finite-size scaling techniques and concepts from the scaling theory of disordered systems to describe the nature of the phase transition of the disordered model, departing gradually from the fixed point of the pure system. Our analysis (based on the determination of the critical exponents) shows that the 3D random-bond Ising model belongs to the same universality class with the site- and bond-dilution models, providing a single universality class for the 3D Ising model with these three types of quenched uncorrelated disorder.