Gibbs measure for mixed spins and mixed types model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917056513835008 |
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| author | Rahmatullaev, Muzaffar Tukhtabaev, Akbarkhuja |
| author_facet | Rahmatullaev, Muzaffar Tukhtabaev, Akbarkhuja |
| contents | In the present paper, we study the $(2,q)$-Ising-Potts model on the Cayley tree. We have derived a recurrence equation that shows the existence of a splitting Gibbs measure for this model. Furthermore, we have proven that for the $(2,q)$-Ising-Potts model on the Cayley tree of order $k\geq2$, there are at least 3 translation-invariant splitting Gibbs measures. We also prove that for the $(2,3)$-Ising-Potts model on the Cayley tree, specifically the binary tree, under certain conditions, there are at least 8 translation-invariant splitting Gibbs measures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_01507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gibbs measure for mixed spins and mixed types model Rahmatullaev, Muzaffar Tukhtabaev, Akbarkhuja Probability Mathematical Physics In the present paper, we study the $(2,q)$-Ising-Potts model on the Cayley tree. We have derived a recurrence equation that shows the existence of a splitting Gibbs measure for this model. Furthermore, we have proven that for the $(2,q)$-Ising-Potts model on the Cayley tree of order $k\geq2$, there are at least 3 translation-invariant splitting Gibbs measures. We also prove that for the $(2,3)$-Ising-Potts model on the Cayley tree, specifically the binary tree, under certain conditions, there are at least 8 translation-invariant splitting Gibbs measures. |
| title | Gibbs measure for mixed spins and mixed types model |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2511.01507 |