Zero-temperature stochastic Ising model on planar quasi-transitive graphs
Probability
2023-10-23 v2 Mathematical Physics
math.MP
Abstract
We study the zero-temperature stochastic Ising model on some connected planar quasi-transitive graphs, which are invariant under rotation and translation. The initial spin configuration is distributed according to a Bernoulli product measure with parameter . In particular, we prove that if and the graph underlying the model satisfies the planar shrink property (which causes each finite cluster to shrink to a site and then vanish with positive probability) then all vertices flip infinitely often almost surely.
Cite
@article{arxiv.2306.16816,
title = {Zero-temperature stochastic Ising model on planar quasi-transitive graphs},
author = {Emilio De Santis and Leonardo Lelli},
journal= {arXiv preprint arXiv:2306.16816},
year = {2023}
}