Dynamical Gibbs-non-Gibbs transitions in the Curie-Weiss Potts model in the regime beta<3

TL;DR

This paper studies how the Curie-Weiss Potts model transitions between Gibbsian and non-Gibbsian states under spin-flip dynamics for inverse temperatures below 3, revealing complex trajectory behaviors and re-entrance phenomena.

Contribution

It provides a detailed analysis of dynamical Gibbs-non-Gibbs transitions in the Curie-Weiss Potts model for beta<3, including classification of trajectories and re-entrance conditions.

Findings

Identification of finitely many trajectory types of bad empirical measures

Re-entrance into the Gibbsian regime under certain conditions

Full description of the transition dynamics for beta<3

Abstract

We consider the Curie-Weiss Potts model in zero external field under independent symmetric spin-flip dynamics. We investigate dynamical Gibbs-non-Gibbs transitions for a range of initial inverse temperatures beta<3, which covers the phase transition point beta=4 log 2 [8]. We show that finitely many types of trajectories of bad empirical measures appear, depending on the parameter beta, with a possibility of re-entrance into the Gibbsian regime, of which we provide a full description.