Review of recent developments in the random-field Ising model

Nikolaos G. Fytas, Victor Martin-Mayor, Marco Picco, Nicolas Sourlas

Published 2017-11-27Version 1

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, critical universality as predicted by perturbative renormalization group is true at three and four dimensions: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. 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.