Potts spin glasses with three, four and five states near T = Tc: expanding around the replica symmetric solution

Expansion for the 1RSB free energy functionals of the mean-field (MF) Potts spin glass models up to the fourth order in δqαβ around the replica symmetric (RS) solution is investigated. We consider models with three, four and five states and use a special quadrupole-like representation for them. The corresponding series for the 1RSB order parameters giving explicit temperature dependence are obtained in the vicinity of the point T = Tc, where the RS solution becomes unstable. The crossover from continuous to jumpwise behavior with increasing number of states is derived analytically. A comparison is made between the free energy expansion for the Potts spin glass and that for other models.