WIAS Preprint No. 2087, (2015)

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


  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Külske, Christof

2010 Mathematics Subject Classification

  • 82B20 82B26


  • Potts models, Kac model, fuzzy Lac-Potts model, Gibbs versus non-Gibbs, large deviation principles, diluted large deviation principles




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 citeFeHoMa14 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. On the way to this result we prove a large deviation principle for color profiles with diluted total mass densities and use monotocity arguments

Appeared in

  • Bernoulli, 23 (2017) pp. 2808--2827.

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