On the static and dynamical transition in the mean-field Potts glass

Abstract

We study the static as well as the glassy or dynamical transition in the mean-field p-state Potts glass. By numerical solution of the saddle-point equations we investigate the static and dynamical transitions for all values of p in the non-perturbative regime p>4. The static and dynamical Edwards-Anderson parameter increase with p logarithmically. This makes the glassy transition temperature lie very close to the static one. We compare the main predictions of the theory with numerical simulations.