A planar Ising model of self-organized criticality

Abstract

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 arXiv:0811.4507, 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.

References in corpus (7)

• The Random-Cluster Model
• The abelian sandpile and related models
• Social Percolation
• Signatures of Self-Organised Criticality in an Ultracold Atomic Gas
• The near-critical planar FK-Ising model
• Infinite volume limit of the Abelian sandpile model in dimensions d >= 3
• A Curie-Weiss model of self-organized criticality

Cited by in corpus (1)

• Some toy models of self-organized criticality in percolation