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arXiv · 2404.03297

Gibbs measures for hardcore-SOS models on Cayley trees

Benedikt Jahnel·Utkir Rozikov
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Abstract

We investigate the finite-state $p$-solid-on-solid model, for $p=\infty$, on Cayley trees of order $k\geq 2$ and establish a system of functional equations where each solution corresponds to a (splitting) Gibbs measure of the model. Our main result is that, for three states, $k=2,3$ and increasing coupling strength, the number of translation-invariant Gibbs measures behaves as $1\to3\to5\to6\to7$. This phase diagram is qualitatively similar to the one observed for three-state $p$-SOS models with $p>0$ and, in the case of $k=2$, we demonstrate that, on the level of the functional equations, the transition $p\to\infty$ is continuous.

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Benedikt Jahnel, Utkir Rozikov. 2024-04-04. Gibbs measures for hardcore-SOS models on Cayley trees. https://arxiv.org/abs/2404.03297

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