Domain Growth and Aging in the Random Field XY Model: A Monte Carlo Study

Abstract

We use large-scale Monte Carlo simulations to obtain comprehensive results for domain growth and aging in the random field XY model in dimensions $d=2,3$. After a deep quench from the paramagnetic phase, the system orders locally via annihilation of topological defects, i.e., vortices and anti-vortices. The evolution morphology of the system is characterized by the correlation function and the structure factor of the magnetization field. We find that these quantities obey dynamical scaling, and their scaling function is independent of the disorder strength $\Delta$. However, the scaling form of the autocorrelation function is found to be dependent on $\Delta$, i.e., superuniversality is violated. The large-$t$ behavior of the autocorrelation function is explored by studying aging and autocorrelation exponents. We also investigate the characteristic growth law $L(t,\Delta)$ in $d=2,3$, which shows an asymptotic logarithmic behavior: $L(t,\Delta) \sim \Delta^{-\varphi} (\ln t)^{1/\psi}$, with exponents $\varphi, \psi > 0$.