- Volume 23, Number 4A (2017), 2808-2827.
Sharp thresholds for Gibbs–non-Gibbs transitions in the fuzzy Potts model with a Kac-type interaction
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.
Bernoulli, Volume 23, Number 4A (2017), 2808-2827.
Received: February 2015
Revised: November 2015
First available in Project Euclid: 9 May 2017
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Jahnel, Benedikt; Külske, Christof. Sharp thresholds for Gibbs–non-Gibbs transitions in the fuzzy Potts model with a Kac-type interaction. Bernoulli 23 (2017), no. 4A, 2808--2827. doi:10.3150/16-BEJ828. https://projecteuclid.org/euclid.bj/1494316833