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

@inproceedings{Forien2021AnEO, title={An extension of the Ising-Curie-Weiss model of self-organized criticality with long range interactions}, author={Nicolas Forien}, year={2021} }

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…

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

- Mathematics
- 2021

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…

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