A curious relationship between Potts glass models

A Potts glass model proposed by Nishimori and Stephen[H. Nishimori and M. J. Stephen, Phys. Rev. B 27, 5644 (1983)] is analyzed by means of the replica mean field theory. This model is a discrete model, has a gauge symmetry, and is called the Potts gauge glass model. By comparing the present results with the results of the conventional Potts glass model, we find the coincidences and differences between the models. We find a coincidence that the property for the Potts glass phase in this model is coincident with that in the conventional model at the mean field level. We find a difference that, unlike in the case of the conventional $p$-state Potts glass model, this system for large $p$ does not become ferromagnetic at low temperature under a concentration of ferromagnetic interaction. The present results support the act of numerically investigating the present model for study of the Potts glass phase in finite dimensions.