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.
Highlights
Dynamical Gibbs–non-Gibbs transitions have attracted much attention over the last years
In zero external magnetic field, the Gibbs property is lost at a finite transition time, after which the measure continues to be nonGibbsian
The present paper is an essential piece in a series of investigations in which we study Gibbs– non-Gibbs transitions of the Widom–Rowlinson model under stochastic spin-flip-dynamics in various geometries
Summary
Dynamical Gibbs–non-Gibbs transitions have attracted much attention over the last years. In this work a strong form of non-Gibbsian behavior, which appears to be more severe than for instance in the case of the Ising model, was found, including full-measure discontinuities of the timeevolved conditional probabilities, and an immediate loss of the Gibbs property. The latter is quite unusual for a lattice model, see the examples in mean-field [2], on a tree [25], and for a transformed measure not coming from a time-evolution in [18].
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