Superuniversality in phase-ordering disordered ferromagnets

TL;DR

This study uses Monte Carlo simulations to explore phase-ordering in disordered ferromagnets, revealing a superuniversality where certain scaling functions depend only on the ratio of disorder strength to temperature.

Contribution

It demonstrates that in disordered ferromagnetic systems, key scaling functions are governed solely by the ratio of disorder width to temperature, indicating a form of superuniversality.

Findings

Dynamical exponent z depends on eps/T

Autocorrelation exponent lambda_C depends on eps/T

Scaling functions depend only on eps/T ratio

Abstract

The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model with uniform bond disorder is investigated by intensive Monte Carlo simulations. Simple ageing behaviour is observed in the single-time correlator and the two-time responses and correlators. The dynamical exponent z and the autocorrelation exponent lambda_C only depend on the ratio eps/T, where eps describes the width of the distribution of the disorder, whereas a more complicated behaviour is found for the non-equilibrium exponent a of the two-time response as well as for the autoresponse exponent lambda_R. The scaling functions are observed to depend only on the dimensionless ratio eps/T. If the length scales are measured in terms of the time-dependent domain size L(t), the form of the scaling functions is in general independent of both eps and T. Conditions limiting the validity of this `superuniversality' are discussed.