Gibbs measure for mixed spins and mixed types model

Muzaffar Rahmatullaev; Akbarkhuja Tukhtabaev

Gibbs measure for mixed spins and mixed types model

Probability 2025-11-04 v1 Mathematical Physics math.MP

Authors: Muzaffar Rahmatullaev , Akbarkhuja Tukhtabaev

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.

Keywords

gibbs measures

Cite

@article{arxiv.2511.01507,
  title  = {Gibbs measure for mixed spins and mixed types model},
  author = {Muzaffar Rahmatullaev and Akbarkhuja Tukhtabaev},
  journal= {arXiv preprint arXiv:2511.01507},
  year   = {2025}
}

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