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Pré-Publication, Document De Travail Année : 2021

An extension of the Ising-Curie-Weiss model of self-organized criticality with a threshold on the interaction range

Une extension du modèle d'Ising Curie-Weiss de criticité auto-organisée avec un phénomène de seuil sur la portée d'interaction

Résumé

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. We study an extension of this model where the mean-field interaction of [CG16] is replaced with a one-dimensional interaction with a certain range dn which varies as a function of the number n of particles. In a previous article [For21], we studied the extreme cases of a very long range of interaction (2dn ∼ λn), which behaves like the mean-field model, and of a nearest neighbour interaction (dn = 1), which does not. In the present article, we study the intermediate regime and we show that the mean-field-like behaviour extends to interaction ranges dn n 3/4 , and we prove that there is a threshold phenomenon with a different behaviour when the interaction range is of order dn n 3/4 .
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Dates et versions

hal-03382821 , version 1 (18-10-2021)
hal-03382821 , version 2 (11-01-2024)

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Nicolas Forien. An extension of the Ising-Curie-Weiss model of self-organized criticality with a threshold on the interaction range. 2021. ⟨hal-03382821v1⟩

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