Universality in Three Dimensional Random-Field Ground States

TL;DR

This study examines the critical behavior of three-dimensional random-field Ising systems with different field distributions, finding that some models share universality class characteristics while others differ significantly.

Contribution

It provides the first comprehensive comparison of critical exponents across different random-field distributions in three-dimensional systems using exact ground-state calculations.

Findings

Gauss and diluted models share the same universality class

Bimodal distribution model exhibits different critical exponents

Finite-size scaling effectively determines critical exponents

Abstract

We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution of random fields and additional the three-dimensional diluted Ising antiferromagnet in an external field. These models are expected to be in the same universality class. We use exact ground-state calculations with an integer optimization algorithm and by a finite-size scaling analysis we calculate the critical exponents nu, beta, and gamma-bar. While the random-field model with Gauss distribution of random fields and the diluted antiferromagnet appear to be in same universality class, the critical exponents of the random-field model with bimodal distribution of random fields seem to be significantly different.