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}
}