Dynamical critical exponents for the mean-field Potts glass

In this paper we study the critical behavior of the fully connected p-color Potts spin glass at the dynamical transition. In the framework of mode coupling theory (MCT), the time autocorrelation function displays a two-step relaxation, with two exponents governing the approach to the plateau and the exit from it. Exploiting a relation between static and equilibrium dynamics which has been recently introduced, we are able to compute the critical slowing down exponents at the dynamical transition with arbitrary precision and for any value of the number of colors p. When available, we compare our exact results with numerical simulations. In addition, we present a detailed study of the dynamical transition in the large p limit, showing that the system is not equivalent to a random energy model.