# Gibbs measures for HC-model with a countable set of spin values on a Cayley tree

@inproceedings{Khakimov2022GibbsMF, title={Gibbs measures for HC-model with a countable set of spin values on a Cayley tree}, author={R. M. Khakimov and M. T. Makhammadaliev and Utkir A. Rozikov}, year={2022} }

. In this paper, we study the HC-model with a countable set Z of spin values on a Cayley tree of order k ≥ 2 . This model is deﬁned by a countable set of parameters (that is, the activity function λ i > 0 , i ∈ Z ). A functional equation is obtained that provides the consistency condition for ﬁnite-dimensional Gibbs distributions. Analyzing this equation, the following results are obtained: - Let Λ = ∑ i λ i . For Λ = +∞ there are no translation-invariant Gibbs measures (TIGM) and no two…

## One Citation

### Periodic points of a $p$-adic operator and their $p$-adic Gibbs measures

- Mathematics
- 2022

. In this paper we investigate generalized Gibbs measure (GGM) for p -adic Hard-Core(HC) model with a countable set of spin values on a Cayley tree of order k ≥ 2. This model is deﬁned by p -adic…

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