English

A planar Ising model of self-organized criticality

Probability 2021-02-22 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2002.08337,
  title  = {A planar Ising model of self-organized criticality},
  author = {Nicolas Forien},
  journal= {arXiv preprint arXiv:2002.08337},
  year   = {2021}
}