Gibbs-non Gibbs transitions in different geometries: The Widom-Rowlinson model under stochastic spin-flip dynamics

TL;DR

This paper investigates how the Widom-Rowlinson model, a particle system with phase transitions, behaves under stochastic spin-flip dynamics across different geometries, focusing on Gibbs-non Gibbs transitions.

Contribution

It provides new insights into the conditions under which the Gibbs property is preserved or lost in dynamical versions of the Widom-Rowlinson model in various geometries.

Findings

Immediate loss of Gibbs property can occur under certain dynamics.

Full-measure discontinuities may develop in the time-evolved models.

Results vary depending on the underlying geometry and parameters.

Abstract

The Widom-Rowlinson model is an equilibrium model for point particles in Euclidean space. It has a repulsive interaction between particles of different colors, and shows a phase-transition at high intensity. Natural versions of the model can moreover be formulated in different geometries: in particular as a lattice system or a mean-field system. We will discuss recent results on dynamical Gibbs-non Gibbs transitions in this context. Main issues will be the possibility or impossibility of an immediate loss of the Gibbs property, and of full-measure discontinuities of the time-evolved models.