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: $L(t,\Delta )\sim {\Delta }^{-\phi }(\ln t{)}^{1/\psi }$, with exponents $\phi ,\psi >0$.

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Cited by in corpus (6)

• Ordering Dynamics of the Random Field Long-range Ising Model in One Dimension
• Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy
• Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity
• Domain Growth in Long-range Ising Models with Disorder
• Dynamical critical behavior on the Nishimori point of frustrated Ising models
• Equilibrium and Nonequilibrium phase transitions in continuous symmetric classical magnets