Dynamical Gibbs–non-Gibbs Transitions in the Curie–Weiss Potts Model in the Regime$$\beta <3$$

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 $$\beta &lt;3$$ β &lt; 3 , which covers the phase transition point $$\beta = 4\log 2$$ β = 4 log 2 (Ellis and Wang in Stoch Process Appl 35(1):59–79, 1990). We show that finitely many types of trajectories of bad empirical measures appear, depending on the parameter $$\beta $$ β , with a possibility of re-entrance into the Gibbsian regime, of which we provide a full description.