Translator Disclaimer
August 2019 Gibbs–non-Gibbs transitions in the fuzzy Potts model with a Kac-type interaction: Closing the Ising gap
Florian Henning, Richard C. Kraaij, Christof Külske
Bernoulli 25(3): 2051-2074 (August 2019). DOI: 10.3150/18-BEJ1045

Abstract

We complete the investigation of the Gibbs properties of the fuzzy Potts model on the $d$-dimensional torus with Kac interaction which was started by Jahnel and one of the authors in (Sharp thresholds for Gibbs-non-Gibbs transitions in the fuzzy Potts model with a Kac-type interaction (2017)). As our main result of the present paper, we extend the previous sharpness result of mean-field bounds to cover all possible cases of fuzzy transformations, allowing also for the occurrence of Ising classes (containing precisely two spin values). The closing of this previously left open Ising-gap involves an analytical argument showing uniqueness of minimizing profiles for certain non-homogeneous conditional variational problems.

Citation

Download Citation

Florian Henning. Richard C. Kraaij. Christof Külske. "Gibbs–non-Gibbs transitions in the fuzzy Potts model with a Kac-type interaction: Closing the Ising gap." Bernoulli 25 (3) 2051 - 2074, August 2019. https://doi.org/10.3150/18-BEJ1045

Information

Received: 1 August 2017; Revised: 1 February 2018; Published: August 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07066249
MathSciNet: MR3961240
Digital Object Identifier: 10.3150/18-BEJ1045

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
24 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.25 • No. 3 • August 2019
Back to Top