Dynamical critical exponents for the mean-field Potts glass

TL;DR

This paper analyzes the critical dynamical exponents of the fully-connected p-colours Potts model at the transition point, providing exact calculations and insights into the large p limit, with comparisons to simulations.

Contribution

It introduces a method to compute critical slowing down exponents precisely for any number of colours p in the Potts glass model.

Findings

Exact critical exponents computed for arbitrary p

Comparison with numerical simulations confirms theoretical results

Large p limit analysis shows non-equivalence to a random energy model

Abstract

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.