On the Static and Dynamical Transition in the Mean-Field Potts Glass

TL;DR

This paper investigates the static and dynamical transitions in the mean-field p-state Potts glass, revealing how the transition points and order parameters behave across different p values through numerical solutions.

Contribution

It provides a detailed numerical analysis of static and dynamical transitions in the mean-field Potts glass for all p>4, highlighting the logarithmic increase of order parameters.

Findings

Static and dynamical Edwards-Anderson parameters increase logarithmically with p.

The glassy transition temperature is very close to the static transition temperature.

Numerical results align with theoretical predictions.

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 the dynamical transition 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 the numerical simulations.