Review of Recent Developments in the Random-Field Ising Model

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

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Pages (from-to)665 - 672
Number of pages8
JournalJournal of Statistical Physics
Volume172
Early online date10 Feb 2018
DOIs
Publication statusPublished - Jul 2018

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Random Field
Ising model
Ising Model
exponents
Antiferromagnet
Dimensional Reduction
Ferromagnet
Ising
Renormalization Group
Critical Exponents
Perturbation Theory
Universality
Three-dimension
Probability Distribution
perturbation theory
Exponent
Numerical Simulation
Prediction
predictions
Review

Bibliographical note

The final publication is available at Springer via http://dx.doi.org/10.1007/s10955-018-1955-7

Keywords

  • Random field Ising models
  • Universality class
  • Optimization methods

Cite this

Review of Recent Developments in the Random-Field Ising Model. / Fytas, Nikolaos; Martin-Mayor, Victor; Picco, Marco; Sourlas, Nicolas.

In: Journal of Statistical Physics, Vol. 172, 07.2018, p. 665 - 672.

Research output: Contribution to journalArticle

Fytas, Nikolaos ; Martin-Mayor, Victor ; Picco, Marco ; Sourlas, Nicolas. / Review of Recent Developments in the Random-Field Ising Model. In: Journal of Statistical Physics. 2018 ; Vol. 172. pp. 665 - 672.
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