Replica symmetry breaking for the mean-field Potts glass model in a field

The mean-field p-state Potts glass model is studied in the presence of a field. As effective ferromagnetic interaction in the Potts glass model grows as temperature decreases, uniform part of the interaction is set to make effective ferromagnetic interaction zero at the continuous glass transition temperature without field. Replica symmetry breaking pattern is obtained analytically near the freezing of the transverse components for small fields. Replica symmetry breaking is continuous for p < 3.4, which is similar to the symmetry breaking for the Ising spin glass model. One step replica symmetry breaking is stable for 3.4 < p < 4.6. The transition to the transverse freezing phase is discontinuous for p > 4.6. This threshold is larger than 4 that is the threshold for the zero field case. These results show that qualitative feature of the transition in a field is similar to that without field if the number of the Potts components is shifted accordingly.