Article

A NEW CLASS OF GIBBS MEASURES FOR THREE-STATE SOS MODEL ON A CAYLEY TREE

M. M. RahmatullaevInstitute of Mathematics named after V. I. RomanovskyBunyod U. AbraevChirchik State Pedagogical Institute of Tashkent Region

Челябинский физико-математический журналjournal2024en

ABI

Abstract

The phase transition phenomenon is one of the central problems of statistical mechanics. It occurs when the model possesses multiple Gibbs measures. In this paper, we consider a three-state SOS (solid-on-solid) model on a Cayley tree. We reduce description of Gibbs measures to solving of a non-linear functional equation, each solution of which corresponds to a Gibbs measure.We give some sufficiency conditions on the existence of multiple Gibbs measures for the model. We give a review of some known (translation-invariant, periodic, non-periodic) Gibbs measures of the model and compare them with our new measures. We show that the Gibbs measures found in the paper differ from the known Gibbs measures, i.e, we show that these measures are new.

Topics

Theoretical and Computational Physics Stochastic processes and statistical mechanics Markov Chains and Monte Carlo Methods

Identifiers

DOI: 10.47475/2500-0101-2024-9-1-101-110

Citations and references

Cited by 10 references

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