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November 2017 Sharp thresholds for Gibbs–non-Gibbs transitions in the fuzzy Potts model with a Kac-type interaction
Benedikt Jahnel, Christof Külske
Bernoulli 23(4A): 2808-2827 (November 2017). DOI: 10.3150/16-BEJ828

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 Fernández, den Hollander and Martínez [J. Stat. Phys. 156 (2014) 203–220] 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.

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Benedikt Jahnel. Christof Külske. "Sharp thresholds for Gibbs–non-Gibbs transitions in the fuzzy Potts model with a Kac-type interaction." Bernoulli 23 (4A) 2808 - 2827, November 2017. https://doi.org/10.3150/16-BEJ828

Information

Received: 1 February 2015; Revised: 1 November 2015; Published: November 2017
First available in Project Euclid: 9 May 2017

zbMATH: 06778257
MathSciNet: MR3648046
Digital Object Identifier: 10.3150/16-BEJ828

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

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Vol.23 • No. 4A • November 2017
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