The Widom-Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality

TL;DR

This paper studies the Gibbs-non-Gibbs transition in the continuum Widom-Rowlinson model under spin-flip dynamics, revealing immediate loss and eventual recovery of quasilocality, with detailed analysis of different symmetry regimes.

Contribution

It provides the first analysis of Gibbs-non-Gibbs transitions for point particles in Euclidean space, showing loss and recovery of quasilocality in the Widom-Rowlinson model.

Findings

Immediate loss of quasilocality in the percolation regime.

Transition from non-quasilocal to Gibbsian regime in color-asymmetric models.

Existence of everywhere quasilocal specifications for all times after the reentrance time.

Abstract

We consider the continuum Widom-Rowlinson model under independent spin-flip dynamics and investigate whether and when the time-evolved point process has an (almost) quasilocal specification (Gibbs-property of the time-evolved measure). Our study provides a first analysis of a Gibbs-non-Gibbs transition for point particles in Euclidean space. We find a picture of loss and recovery, in which even more regularity is lost faster than it is for time-evolved spin models on lattices. We show immediate loss of quasilocality in the percolation regime, with full measure of discontinuity points for any specification. For the color-asymmetric percolating model, there is a transition from this non-a.s. quasilocal regime back to an everywhere Gibbsian regime. At the sharp reentrance time $t_G>0$ the model is a.s. quasilocal. For the color-symmetric model there is no reentrance. On the constructive side, for all $t>t_G$, we provide everywhere quasilocal specifications for the time-evolved measures and give precise exponential estimates on the influence of boundary conditions.