Color symmetry breaking in the Potts spin glass

TL;DR

This paper investigates the color symmetry properties of the Potts spin glass model, revealing that the previously assumed invariance under color permutations fails for models with 58 or more colors.

Contribution

The study disproves the conjecture that the Potts spin glass's order parameter remains invariant under color permutations for large numbers of colors, specifically when 658.

Findings

Color symmetry breaking occurs for 658 or more colors.

The invariance of the order parameter does not hold universally.

Provides a counterexample to previous symmetry assumptions.

Abstract

The Potts spin glass is an analogue of the Sherrington-Kirkpatrick model in which each spin can take one of $\kappa$ possible values, which we interpret as colors. It was suggested in arXiv:2310.06745 that the order parameter for this model is always invariant with respect to permutations of the colors. We show here that this is false whenever $\kappa \ge 58$.