THE WIDOM–ROWLINSON MODEL UNDER SPIN FLIP: IMMEDIATE LOSS AND SHARP RECOVERY OF QUASILOCALITY

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 transit...

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Bibliographic Details
Published in:The Annals of applied probability 2017-12, Vol.27 (6), p.3845-3892
Main Authors: Jahnel, Benedikt, Külske, Christof
Format: Article
Language:English
Subjects:
Analysis
Asymmetry
Color
Euclidean geometry
Euclidean space
Lattice theory
Lattices
Percolation
Recovery
Specifications
Spin dynamics
Time measurement
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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 tG > 0, the model is a.s. quasilocal. For the color-symmetric model, there is no reentrance. On the constructive side, for all t > tG, we provide everywhere quasilocal specifications for the time-evolved measures and give precise exponential estimates on the influence of boundary condition.
ISSN:1050-5164
2168-8737
DOI:10.1214/17-AAP1298