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 .
Domaines
Probabilités [math.PR]
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Ising_model_of_SOC_threshold_on_interaction_range.pdf (552.32 Ko)
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