Is SU(2) lattice gauge theory a spin glass?

TL;DR

This paper introduces a novel order parameter for SU(2) lattice gauge theory that detects a spin glass transition without gauge fixing, indicating a possible second transition at higher coupling.

Contribution

It develops a new gauge-invariant order parameter using the two-replica method to identify spin glass behavior in SU(2) lattice gauge theory.

Findings

Detected a spin glass transition at 6 with a critical exponent .99

Observed spontaneous Z2 symmetry breaking without gauge fixing

Suggests a second transition from spin glass to ferromagnet at higher 

Abstract

A new order parameter is constructed for SU(2) lattice gauge theory in the context of the two-real-replica method normally used for spin glasses. The order parameter is sensitive to a global Z2 subgroup of the gauge symmetry which is seen to break spontaneously at $\beta = 4/g^2 = 1.96\pm 0.01$. No gauge fixing is required. Finite size scaling is consistent with a high-order paramagnet to spin glass transition with a critical exponent $\nu = 0.99 \pm 0.13$. The existence of this transition suggests a second transition from spin glass to ferromagnet should exist at higher $\beta$.