The Widom--Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality
- Jahnel, Benedikt
- Külske, Christof
2010 Mathematics Subject Classification
- 82C21 60K35
- Gibbsianness, non-Gibbsianness, point processes, Widom-Rowlinson model, spin-flip dynamics, quasilocality, non almost-sure quasilocality, -topology
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 tG> 0 the model is a.s. quasilocal. For the colorsymmetric 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 conditions.
- Ann. Appl. Probab., 27 (2017), pp. 3845--3892, DOI 10.1214/17-AAP1298 .