Monte Carlo Simulations of Vector Spin Glasses at Low Temperatures

TL;DR

This paper uses parallel tempering Monte Carlo simulations to study low-temperature behaviors of three- and four-dimensional vector spin glasses, revealing finite-energy large-scale excitations and complex surface structures.

Contribution

It provides new simulation results on vector spin glasses, suggesting finite-energy excitations and exploring their surface properties, with implications for replica symmetry breaking scenarios.

Findings

Large-scale excitations may have finite energy in the thermodynamic limit.

Surface of excitations is fractal, but could be space-filling in some cases.

Results are consistent with earlier work on Ising spin glasses.

Abstract

In this paper I report results for simulations of the three-dimensional gauge glass and the four-dimensional XY spin glass using the parallel tempering Monte Carlo method at low temperatures for moderate sizes. The results are qualitatively consistent with earlier work on the three- and four-dimensional Edwards-Anderson Ising spin glass. I find evidence that large-scale excitations may cost only a finite amount of energy in the thermodynamic limit. The surface of these excitations is fractal, but I cannot rule out for the XY spin glass a scenario compatible with replica symmetry breaking where the surface of low-energy large-scale excitations is space filling.