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Dynamical critical exponents for the mean-field Potts glass

In this paper we study the critical behaviour of the fully-connected p-colours Potts model 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 statics 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 colours 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.