Zero-Temperature Stochastic Ising Model on Planar Quasi-Transitive Graphs

Abstract

We study the zero-temperature stochastic Ising model on some connected planar quasi-transitive graphs, which are invariant under rotations and translations. The initial spin configuration is distributed according to a Bernoulli product measure with parameter \( p\in (0,1) \). In particular, we prove that if \( p=1/2 \) and the graph underlying the model satisfies the planar shrink property then all vertices flip infinitely often almost surely.