An extension of the Ising-Curie-Weiss model of self-organized criticality with long range interactions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910294312222720 |
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| author | Forien, Nicolas |
| author_facet | Forien, Nicolas |
| contents | 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 d(n) 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 (d(n) of order n), the model exhibits the same behaviour as in the mean-field case, whereas in the case of a nearest neighbour interaction (d(n) = 1), the behaviour highlighted by Cerf and Gorny breaks out. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_07948 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An extension of the Ising-Curie-Weiss model of self-organized criticality with long range interactions Forien, Nicolas Probability 82B20 (Primary) 82B27, 60K35 (Secondary) 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 d(n) 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 (d(n) of order n), the model exhibits the same behaviour as in the mean-field case, whereas in the case of a nearest neighbour interaction (d(n) = 1), the behaviour highlighted by Cerf and Gorny breaks out. |
| title | An extension of the Ising-Curie-Weiss model of self-organized criticality with long range interactions |
| topic | Probability 82B20 (Primary) 82B27, 60K35 (Secondary) |
| url | https://arxiv.org/abs/2110.07948 |