Review of recent developments in the random-field Ising model
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.
Cite
@article{arxiv.1711.09597,
title = {Review of recent developments in the random-field Ising model},
author = {Nikolaos G. Fytas and Victor Martin-Mayor and Marco Picco and Nicolas Sourlas},
journal= {arXiv preprint arXiv:1711.09597},
year = {2018}
}
Comments
11 pages, 4 figures, updated and extended version, to be published in J. Stat. Phys