Dynamical Gibbs-non-Gibbs transitions in the Curie-Weiss Potts model in the regime beta&lt;3

Kuelske, Christof; Meissner, Daniel

doi:10.48550/arxiv.2011.00350

Cited by 1 publication

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References 27 publications

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“…This study of the Ising model has been extended to mean-field and Kac-models, where the appropriate notion of sequential Gibbsianness has been employed [8,9,16,24]. For studies of Gibbsian properties of the Potts model under time evolution and also other transformations, see [12,13,14,25].…”

Section: Introductionmentioning

confidence: 99%

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

Bergmann¹,

Kissel²,

Kuelske³

2020

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We consider the soft-core Widom-Rowlinson model for particles with spins and holes, on a Cayley tree of degree d, 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.

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