Equilibrium state of the mean-field Potts glass

We investigate the low-temperature equilibrium state of the p-state mean-field Potts glass. It is the presently believed that there is a temperature interval T-2 < T < T-c within which the equilibrium state for p > p* approximate to 2.82 is described by the cavity method corresponding to the first level of replica-symmetry breaking. We demonstrate that this locally stable solution is globally unstable and that true equilibrium in the region of instability of the replica-symmetric solution (T < T-c), marked by the highest free energy, is a state displaying a continuous replica-symmetry breaking.