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.

11 pages, 4 figures, updated and extended version, to be published in J. Stat. Phys

References in corpus (4)

• Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions
• Restoration of dimensional reduction in the random-field Ising model at five dimensions
• Diluted Antiferromagnetic 3D Ising model in a field
• Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model

Cited by in corpus (20)

• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• Ordered magnetism in the intrinsically decorated $j{}_{\mathrm{eff}}$ = $\frac{1}{2}$ $\alpha$-CoV${}_3$O${}_8$
• Low-dimensional dynamics of phase oscillators driven by Cauchy noise
• Finite-size scaling of the random-field Ising model above the upper critical dimension
• Dimensional Reduction by Conformal Bootstrap
• Critical behavior of the spin-3/2 Blume Capel quantum model with two random transverse single-ion anisotropies
• Nonequilibrium Multiple Transitions in the Core-shell Ising Nanoparticles Driven by Randomly Varying Magnetic Fields
• Thermal vestiges of avalanches in the driven random field Ising model
• Effects of random fields on the reversal of magnetisation of Ising ferromagnet
• Dimensional reduction breakdown and correction to scaling in the random-field Ising model
• On the critical exponent $\alpha$ of the 5D random-field Ising model
• Temperature dependence of the $(\pi ,0)$ anomaly in the excitation spectrum of the 2D quantum Heisenberg antiferromagnet
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• Theoretical studies on switching of magnetisation in thin film
• Kinetic Random-Field Nonreciprocal Ising Model
• Domain Growth in Long-range Ising Models with Disorder
• Empirical validation of the polarization transition in a double-random field model of elections
• Rejection-free Glauber Monte Carlo for the 2D Random Field Ising Model via Hierarchical Probabilistic Counters
• The Schwartz-Soffer and more inequalities for random fields
• Behavior of the Random Field $XY$ Model on Simple Cubic Lattices at $h_r=1.5$