Abstract
Ordered phase and first-order transition are investigated for the infinite-range Potts-glass model. A convergence condition of the free energy for the Thouless, Anderson, and Palmer (TAP) mean-field theory is obtained. Solutions for the mean-field equations in the TAP approach are obtained numerically for p=5 where p is the number of the Potts states. A class of solutions with partially restored permutation symmetry for the Potts index is found. Interpretation of these solutions in the replica approach is given. The first-order transition does not occur by crossing of the paramagnetic and the glass free energies. The free energy of the glass phase is always larger than that of the paramagnetic phase as has been suggested by the replica approach. Confluence of solutions with a rise in temperature for the glass phase seldom occurs in contrast with the Ising case.
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