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Pré-publication, Document de travail

An extension of the Ising-Curie-Weiss model of self-organized criticality with long range interactions

Abstract : In [CG16], Cerf and Gorny constructed a model of self-organized criticality, by introducing an automatic control of the temperature parameter in the generalized Ising Curie-Weiss model. In this article, we build upon this model by replacing the mean-field interaction of [CG16] with a one-dimensional interaction with a certain range dn which varies as a function of the number n of particles. In the Gaussian case, we show that, for a very long range of interaction (2dn ∼ λn), the model exhibits the same behaviour as in the mean-field case, whereas in the case of a nearest neighbour interaction (dn = 1), the behaviour highlighted by Cerf and Gorny breaks out.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-03382815
Contributeur : Nicolas Forien Connectez-vous pour contacter le contributeur
Soumis le : lundi 18 octobre 2021 - 12:36:06
Dernière modification le : mardi 19 octobre 2021 - 22:59:46

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  • HAL Id : hal-03382815, version 1
  • ARXIV : 2110.07948

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Nicolas Forien. An extension of the Ising-Curie-Weiss model of self-organized criticality with long range interactions. 2021. ⟨hal-03382815⟩

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