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arXiv · 2306.16816

Zero-temperature stochastic Ising model on planar quasi-transitive graphs

Emilio De Santis·Leonardo Lelli
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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\in(0,1) $. In particular, we prove that if $ 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.

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Emilio De Santis, Leonardo Lelli. 2023-06-29. Zero-temperature stochastic Ising model on planar quasi-transitive graphs. https://doi.org/10.1007/s10955-023-03177-5

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