Gibbs measure for mixed spins and mixed types model

Muzaffar Rahmatullaev; Akbarkhuja Tukhtabaev

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arXiv · 2511.01507

Gibbs measure for mixed spins and mixed types model

Muzaffar Rahmatullaev·Akbarkhuja Tukhtabaev

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Abstract

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.

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BibTeX RIS

Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev. 2025-11-03. Gibbs measure for mixed spins and mixed types model. https://arxiv.org/abs/2511.01507

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