Mean-field Theory of Potts Glass Revised

Abstract: We investigate the p-state mean-field model of the Potts glass for 2 < p < 4 below the continuous phase transition to the glassy phase. It is generally believed that the first replica symmetry breaking solution describes the low temperature equilibrium state. We find out apart from a solution with the first hierarchical level of replica-symmetry breaking, which is locally stable close to the transition point, another hierarchical solution that in the limit of the infinitely breaking symmetry scheme agrees with the continuous full replica-symmetry breaking solution (FRSB). The latter is marginally stable and has higher free energy than the former. We argue that the true equilibrium is reached only by FRSB being globally stable.