GENERALIZED CURIE-WEISS MODEL AND QUADRATIC PRESSURE IN ERGODIC THEORY

Abstract : We explain the Curie Weiss model in Statistical Mechanics within the Ergodic viewpoint. More precisely, we simultaneously define in {−1, +1} N , on the one hand a generalized Curie Weiss model within the Statistical Mechanics viewpoint and on the other hand, quadratic free energy and quadratic pressure within the Ergodic Theory viewpoint. We show that there are finitely many invariant measures which maximize the quadratic free energy. They are all Dynamical Gibbs Measures. Moreover, the Probabilistic Gibbs measures for generalized Curie Weiss model converge to a determined combination of the (dynamical) conformal measures associated to these Dynamical Gibbs Measures. The standard Curie Weiss model is a particular case of our generalized Curie Weiss model. An Ergodic viewpoint over the Curie Weiss Potts model is also given.
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Pré-publication, Document de travail
2018
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Contributeur : Renaud Leplaideur <>
Soumis le : mardi 9 janvier 2018 - 01:01:17
Dernière modification le : jeudi 11 janvier 2018 - 06:25:25

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Renaud Leplaideur, Frédérique Watbled. GENERALIZED CURIE-WEISS MODEL AND QUADRATIC PRESSURE IN ERGODIC THEORY. 2018. 〈hal-01678176〉

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