2021/01/01 by Nicolas Forien, Forien, Nicolas
Materials Science · Mathematics · Physics and Astronomy · #60K35 (Secondary) #82B20 (Primary) 82B27 #FOS: Mathematics #Material Dynamics and Properties #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2110.07948
openalex publication_date 2021/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.