Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts model with a Kac-type interaction

2015/02/14 by Benedikt Jahnel, B. Jahnel, Jahnel, B. +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1502.04238

20 pages

openalex publication_date 2015/02/14 · arxiv created 2016/02/18 · arxiv updated 2016/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the Gibbs properties of the fuzzy Potts model on the d-dimensional torus with Kac interaction. We use a variational approach for profiles inspired by that of Fernandez, den Hollander and Martınez for their study of the Gibbs-non-Gibbs transitions of a dynamical Kac-Ising model on the torus. As our main result, we show that the mean-field thresholds dividing Gibbsian from non-Gibbsian behavior are sharp in the fuzzy Kac-Potts model with class size unequal two. On the way to this result we prove a large deviation principle for color profiles with diluted total mass densities and use monotocity arguments.

Citations

• Some generalized order-disorder transformations

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