Continuous RSB mean-field solution of the Potts glass

TL;DR

This paper analyzes the mean-field Potts glass model with 2 to 4 states, revealing both 1RSB and FRSB solutions, and argues that the true equilibrium corresponds to the FRSB phase due to its global thermodynamic stability.

Contribution

It provides a continuous full replica-symmetry breaking solution for the Potts glass, extending understanding of its phase structure beyond the 1RSB approximation.

Findings

FRSB solution is marginally stable and has higher free energy than 1RSB.

True equilibrium state is described by FRSB, which is globally thermodynamically homogeneous.

Both 1RSB and FRSB solutions exist near the transition point.

Abstract

We investigate the p-state mean-field model of the Potts glass ($2\le p \le 4$) below the continuous phase transition to a glassy phase. We find that apart from a solution with a first hierarchical level of replica-symmetry breaking (1RSB), locally stable close to the transition point, there is a continuous full replica-symmetry breaking (FRSB) solution. The latter is marginally stable and has a higher free energy than the former. We argue that the true equilibrium is reached only by FRSB, being globally thermodynamically homogeneous, whereas 1RSB is only locally homogeneous.