Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States

For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the lower relative entropy density. As a consequence, we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting....

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Detalles Bibliográficos
Autores principales: Chazottes, Jean-René, Redig, Frank
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9689258/
https://www.ncbi.nlm.nih.gov/pubmed/36359606
http://dx.doi.org/10.3390/e24111513
Descripción
Sumario:For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the lower relative entropy density. As a consequence, we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting. This extends earlier results with a different and very short proof.

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