Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction: Closing the Ising gap

Florian Henning; Richard Kraaij; Christof Külske

doi:10.3150/18-BEJ1045

Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction: Closing the Ising gap

Florian Henning, Richard Kraaij, Christof Külske

Research output: Contribution to journal › Article › Scientific › peer-review

6 Citations (Scopus)

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 [JaKu17]. 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.

Original language	English
Pages (from-to)	2051-2074
Number of pages	23
Journal	Bernoulli: a journal of mathematical statistics and probability
Volume	25
Issue number	3
DOIs	https://doi.org/10.3150/18-BEJ1045
Publication status	Published - 2019
Externally published	Yes

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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 [JaKu17]. 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. ",

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AU - Kraaij, Richard

AU - Külske, Christof

PY - 2019

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AB - 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 [JaKu17]. 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.

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DO - 10.3150/18-BEJ1045

M3 - Article

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JF - Bernoulli: a journal of mathematical statistics and probability

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ER -

Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction: Closing the Ising gap

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