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

Abstract

AbstractWe 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 $$ p\in (0,1) $$ p ∈ ( 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 then all vertices flip infinitely often almost surely.