## Bernoulli

• Bernoulli
• Volume 23, Number 4A (2017), 2808-2827.

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

#### 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.

#### Article information

Source
Bernoulli, Volume 23, Number 4A (2017), 2808-2827.

Dates
Revised: November 2015
First available in Project Euclid: 9 May 2017

https://projecteuclid.org/euclid.bj/1494316833

Digital Object Identifier
doi:10.3150/16-BEJ828

Mathematical Reviews number (MathSciNet)
MR3648046

Zentralblatt MATH identifier
06778257

#### Citation

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

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