A planar Ising model of self-organized criticality

Un modèle d'Ising de criticité auto-organisée en dimension 2

Nicolas Forien (1, 2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 DMA - Département de Mathématiques et Applications - ENS Paris

We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the system towards the critical point. Using the finite-size scaling results of [CM11], we show that, when the size of the box grows to infinity, the temperature concentrates around the critical temperature of the planar Ising model on the square lattice.

Domaines: Mathématiques [math]; Physique mathématique [math-ph]; Probabilités [math.PR]

Nicolas Forien. A planar Ising model of self-organized criticality. 2020. ⟨hal-02488153v1⟩