Article

Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree

M. M. RakhmatullaevRomanovsky Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Tashkent, UzbekistanBegzod Mukhtorjonovich IsakovAndizhan State University, Andizhan, Uzbekistan

Theoretical and Mathematical Physicsjournal2024en

ABI

Abstract

We consider a mixed-type model given by the three-state Ising–Potts model on a Cayley tree. A criterion for the existence of limit Gibbs measures for this model on an arbitrary-order Cayley tree is obtained. Translation-invariant Gibbs measures on a second-order Cayley tree are studied. The existence of a phase transition is proved: a range of parameter values is found in which there are one to seven Gibbs measures for the three-state Ising–Potts model.

Topics

Theoretical and Computational Physics Opinion Dynamics and Social Influence Markov Chains and Monte Carlo Methods

Identifiers

DOI: 10.1134/s0040577924060114

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