The Lower Critical Dimension of the XY Spin Glass

TL;DR

This study uses the domain-wall renormalization-group method to analyze the XY spin-glass model, suggesting the lower critical dimension for spin-glass ordering is around three, challenging previous beliefs of four.

Contribution

It provides new numerical evidence indicating the lower critical dimension for XY spin glasses may be lower than previously thought, around three instead of four.

Findings

Lower critical dimension for XY spin glasses is approximately 3.

3D data suggest a finite spin-glass transition temperature.

Results are compatible with the system being at or below its lower critical dimension.

Abstract

We investigate the XY spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to L=12 (2D) and L=8 (3D) strongly suggest that the lower critical dimension for spin-glass ordering may be $d_{c}\approx 3$ rather than four as is commonly believed. Our 3D data favor the scenario of a low but finite spin-glass ordering temperature below the chiral transition but they are also compatible with the system being at or slightly below its lower critical dimension.