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

TL;DR

This study uses large-scale Monte Carlo simulations to analyze domain growth and aging in the random field XY model across two and three dimensions, revealing scaling behaviors, violations of superuniversality, and logarithmic growth laws.

Contribution

It provides the first comprehensive simulation-based analysis of domain growth and aging in the random field XY model, highlighting the violation of superuniversality and the logarithmic growth law.

Findings

Correlation and structure factor obey dynamical scaling, independent of disorder.

Autocorrelation function scaling depends on disorder strength, violating superuniversality.

Domain size grows logarithmically with time, with disorder-dependent exponents.

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 $\varphi, \psi > 0$.