# Dynamical Gibbs-non-Gibbs transitions in lattice Widom-Rowlinson models with hard-core and soft-core interactions

## TL;DR

This paper studies how lattice Widom-Rowlinson models with hard-core and soft-core interactions undergo dynamical Gibbs-non-Gibbs transitions under spin-flip dynamics, revealing different temporal behaviors despite similar equilibrium phase transitions.

## Contribution

It compares the dynamical Gibbs properties of hard-core and soft-core Widom-Rowlinson models on the lattice, highlighting their distinct time-evolution behaviors.

## Key findings

- Soft-core model remains Gibbs for small times, loses Gibbs for large times.
- Hard-core model loses Gibbs immediately, then can regain it at a sharp transition time.
- Both models exhibit similar phase transitions in equilibrium but differ dynamically.

## Abstract

We consider the Widom-Rowlinson model on the lattice $\mathbb{Z}^d$ in two versions, comparing the cases of a hard-core repulsion and of a soft-core repulsion between particles carrying opposite signs. For both versions we investigate their dynamical Gibbs-non-Gibbs transitions under an independent stochastic symmetric spin-flip dynamics. While both models have a similar phase transition in the high-intensity regime in equilibrium, we show that they behave differently under time-evolution: The time-evolved soft-core model is Gibbs for small times and loses the Gibbs property for large enough times. By contrast, the time-evolved hard-core model loses the Gibbs property immediately, and for asymmetric intensities, shows a transition back to the Gibbsian regime at a sharp transition time.