Ordering Kinetics in the Random Bond XY Model

TL;DR

This study uses Monte Carlo simulations to analyze how quenched disorder affects domain growth in the random-bond XY model across two and three dimensions, revealing disorder-dependent growth laws and breakdown of superuniversality.

Contribution

It provides the first detailed Monte Carlo analysis of domain growth in the disordered XY model, highlighting disorder-dependent growth laws and the breakdown of superuniversality.

Findings

Power-law growth with disorder-dependent exponents in 2D

Logarithmic growth regime in 3D

Scaling functions are disorder-independent for correlations, but not for autocorrelations

Abstract

We present a comprehensive Monte Carlo study of domain growth in the random-bond XY model with non-conserved kinetics. The presence of quenched disorder slows down domain growth in d = 2; 3. In d = 2, we observe power-law growth with a disorder-dependent exponent on the time-scales of our simulation. In d = 3, we see the signature of an asymptotically logarithmic growth regime. The scaling functions for the real-space correlation function are seen to be independent of the disorder. However, the same does not apply for the two-time autocorrelation function, demonstrating the breakdown of superuniversality.