Review of recent developments in the random-field Ising model

TL;DR

Recent large-scale simulations have advanced understanding of the random-field Ising model, confirming critical universality across distributions and dimensions, and restoring dimensional reduction at five dimensions.

Contribution

This review highlights new numerical evidence supporting critical universality and dimensional reduction in the random-field Ising model.

Findings

Critical exponents are universal across different distributions.

Dimensional reduction is valid at five dimensions.

Universality extends beyond perturbative regimes.

Abstract

A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same.