Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model

TL;DR

This study investigates the phase ordering dynamics of the 2D and 3D random field Ising model, revealing a crossover from power-law to logarithmic growth and showing that superuniversality does not hold, contrary to some previous claims.

Contribution

It provides a detailed analysis confirming the crossover to logarithmic growth and demonstrates the disorder dependence of the preasymptotic power law, challenging earlier assumptions of superuniversality.

Findings

Confirmed crossover to logarithmic growth

Discovered disorder-dependent preasymptotic power law

Autocorrelation function lacks superuniversality

Abstract

We study the nonconserved phase ordering dynamics of the d = 2, 3 random field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three di- mensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, the exponent in the preasymptotic power law is disorder-dependent, rather than being the one of the pure system. Furthermore, we find that the autocorre- lation function does not display superuniversal behavior. This restores consistency with previous results for the d = 1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random bond Ising model.