Ultraslow Growth of Domains in a Random-Field System With Correlated Disorder

TL;DR

This paper investigates the extremely slow, double logarithmic growth of magnetic domains in a random-field system with spatially correlated disorder, using simulations to analyze domain morphology and growth kinetics.

Contribution

It introduces a detailed simulation study of domain growth in correlated random-field systems, revealing ultraslow growth behavior and domain morphology characteristics.

Findings

Domain growth follows a double logarithmic law.

Porod's law holds for the structure factor at large wave numbers.

Domains exhibit specific morphological features during evolution.

Abstract

We study domain growth kinetics in a random-field system in the presence of a spatially correlated disorder $h_{i}(\vec r)$ after an instantaneous quench at a finite temperature $T$ from a random initial state corresponding to $T=\infty$. The correlated disorder field $h_{i}(\vec r)$ arises due to the presence of magnetic impurities, decaying spatially in a power-law fashion. We use Glauber spin-flip dynamics to simulate the kinetics at the microscopic level. The system evolves via the formation of ordered magnetic domains. We characterize the morphology of domains using the equal-time correlation function $C(r,t)$ and structure factor $S(k,t)$. In the large-$k$ limit, $S(k, t)$ obeys Porod's law: $S(k, t)\sim k^{-(d+1)}$. The average domain size $L(t)$ asymptotically follows \textit{double logarithmic growth behavior}.