Dynamical Gibbs–non-Gibbs transitions in Widom–Rowlinson models on trees

4Citations
Citations of this article
1Readers
Mendeley users who have this article in their library.
Get full text

Abstract

We consider the soft-core Widom–Rowlinson model for particles with spins and holes, on a Cayley tree of order d (which has d + 1 nearest neighbours), depending on repulsion strength β between particles of different signs and on an activity parameter λ for particles. We analyse Gibbsian properties of the time-evolved intermediate Gibbs measure of the static model, under a spin-flip time evolution, in a regime of large repulsion strength β. We first show that there is a dynamical transition, in which the measure becomes non-Gibbsian at large times, independently of the particle activity, for any d ≥ 2. In our second and main result, we also show that for large β and at large times, the measure of the set of bad configurations (discontinuity points) changes from zero to one as the particle activity λ increases, assuming that d ≥ 4. Our proof relies on a general zero-one law for bad configurations on the tree, and the introduction of a set of uniformly bad configurations given in terms of subtree percolation, which we show to become typical at high particle activity.

Cite

CITATION STYLE

APA

Bergmann, S., Kissel, S., & Külske, C. (2023). Dynamical Gibbs–non-Gibbs transitions in Widom–Rowlinson models on trees. Annales de l’institut Henri Poincare (B) Probability and Statistics, 59(1), 325–344. https://doi.org/10.1214/22-AIHP1242

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free