Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets

TL;DR

This paper investigates domain growth in disordered ferromagnets, revealing a crossover from power-law to logarithmic growth and showing that super-universality does not hold, with results supported by a renormalization group framework.

Contribution

It provides comprehensive numerical analysis of the 2D Random Bond Ising Model, identifying a crossover in growth laws and challenging the super-universality hypothesis.

Findings

Growth law crosses from power-law to logarithmic behavior

Super-universality does not hold in disordered ferromagnets

Scaling exponent of autoresponse function depends on dimensionality

Abstract

We present comprehensive numerical results for domain growth in the two-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauber kinetics. We characterize the evolution via the {\it domain growth law}, and two-time quantities like the {\it autocorrelation function} and {\it autoresponse function}. Our results clearly establish that the growth law shows a crossover from a pre-asymptotic regime with "power-law growth with a disorder-dependent exponent" to an asymptotic regime with "logarithmic growth". We compare this behavior with previous results on one-dimensional disordered systems and we propose a unifying picture in a renormalization group framework. We also study the corresponding crossover in the scaling functions for the two-time quantities. Super-universality is found not to hold. Clear evidence supporting the dimensionality dependence of the scaling exponent of the autoresponse function is obtained.