• Corpus ID: 248512507

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… 
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