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

Source: [Ultraslow Growth of Domains in a Random-Field System With Correlated Disorder](<https://www.sota2.com/research/paper/68fa4a361e209131ce93caa2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T07:42:50.580Z

Authors: Subhanker Howlader, Prasenjit Das, Manoj Kumar

Published: 2025-05-11T06:49:19.000Z

## 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}.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2505.06873>)

[PDF](<https://arxiv.org/pdf/2505.06873.pdf>)