An extension of the IsingCurieWeiss model of selforganized criticality with long range interactions
Abstract
In [CG16], Cerf and Gorny constructed a model of selforganized criticality, by introducing an automatic control of the temperature parameter in the generalized Ising CurieWeiss model. In this article, we build upon this model by replacing the meanfield interaction of [CG16] with a onedimensional 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 meanfield case, whereas in the case of a nearest neighbour interaction (d(n) = 1), the behaviour highlighted by Cerf and Gorny breaks out.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.07948
 Bibcode:
 2021arXiv211007948F
 Keywords:

 Mathematics  Probability;
 82B20 (Primary) 82B27;
 60K35 (Secondary)
 EPrint:
 53 pages