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

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 $T=\mathrm{\infty }$. 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 $\mathit{\text{double}}\mathit{\text{logarithmic}}\mathit{\text{growth}}\mathit{\text{behavior}}$.