Gibbs measures for hardcore-SOS models on Cayley trees
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913298729926656 |
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| author | Jahnel, Benedikt Rozikov, Utkir |
| author_facet | Jahnel, Benedikt Rozikov, Utkir |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_03297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gibbs measures for hardcore-SOS models on Cayley trees Jahnel, Benedikt Rozikov, Utkir Mathematical Physics 82B26, 60K35 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. |
| title | Gibbs measures for hardcore-SOS models on Cayley trees |
| topic | Mathematical Physics 82B26, 60K35 |
| url | https://arxiv.org/abs/2404.03297 |