English

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 p(0,1) p\in(0,1) . In particular, we prove that if p=1/2 p=1/2 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.

Keywords

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}
}
R2 v1 2026-06-28T11:17:44.426Z