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

By Benedikt Jahnel and Christof Kuelske

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.Comment: 36 pages, 4 figures, 1 tabl

Topics: Mathematics - Probability, 82C21 (Primary), 60K35 (Secondary)
Year: 2017
OAI identifier: oai:arXiv.org:1609.01328

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