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The Widom – Rowlinson model under spin flip: immediate loss and sharp recovery of quasilocality. (English) Zbl 1390.82039
Summary: 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-almost-sure 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 condition.

MSC:
82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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