Large-scale Monte Carlo simulations of the three-dimensional XY spin glass

TL;DR

This study uses large-scale Monte Carlo simulations to investigate the three-dimensional XY spin glass, revealing that the lower critical dimension is near three and that spins and chiralities exhibit similar behaviors.

Contribution

It provides extensive simulation data for larger system sizes, offering new insights into the critical behavior and marginality of the XY spin glass in three dimensions.

Findings

Lower critical dimension is close to three.

Spins and chiralities behave similarly.

Optimal simulation parameters identified.

Abstract

We study the XY spin glass by large-scale Monte Carlo simulations for sizes up to 24^3, down to temperatures below the transition temperature found in earlier work. The data for the larger sizes show more marginal behavior than that for the smaller sizes indicating that the lower critical dimension is close to, and possibly equal to three. We find that the spins and chiralities behave in a very similar manner. We also address the optimal ratio of "over-relaxation" to "Metropolis" sweeps in the simulation.