Uncountably many extremal Series--Sinai states for the Ising model on Lobachevsky lattices

Jean Vereecke

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arXiv · 2607.08632

Uncountably many extremal Series--Sinai states for the Ising model on Lobachevsky lattices

Jean Vereecke

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Abstract

We construct an uncountable family of extremal Gibbs states of the low temperature Ising model on hyperbolic lattices embedded in the hyperbolic plane $\mathbb{H}_2$ whose interfaces are complete geodesics of $\mathbb{H}_2$. These states are extracted from the states constructed by D'Achille, Coquille and Le Ny in arXiv:2504.19553v2 by considering path in the dual lattice at close enough distance from geodesics of $\mathbb{H}_2$ thanks to the Morse--Mostow lemma.

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Jean Vereecke. 2026-07-09. Uncountably many extremal Series--Sinai states for the Ising model on Lobachevsky lattices. https://arxiv.org/abs/2607.08632

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