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We expand asymptotically mean-field solutions of the $p<4$ Potts glass withvarious levels of replica-symmetry breaking below the transition temperature tothe glassy phase. We find that the ordered phase is degenerate and solutionswith one hierarchy of spin replicas and with the full continuousreplica-symmetry breaking coexist for $p> p^{*} \approx 2.82$. The latteremerges immediately with the instability of the replica-symmetric one. Apartfrom these two solutions there exists also a succession of unstable statesconverging to the solution with the continuous replica-symmetry breaking thatis marginally stable and has the highest free energy.

Mean-field solution of the Potts glass near the transition temperature to the ordered phase