arXiv subjects

Rustam Khakimov

Publications and source records attributed to Rustam Khakimov.

4 recordsLinked to original sources

arXiv2015

Translation-invariant and weakly periodic Gibbs measures for HC-models on a Cayley tree

In this paper is studied HC-models on a Cayley tree. two states HC-model on a Cayley tree and Under some conditions on parameters of the two state HC-model we prove existence exactly two of the weakly periodic (non periodic) Gibbs measures. Furthermore, it considered translation-invariant Gibbs measures for fertile four state HC-models and for one of them it proved the non-uniqueness of the translation-invariant Gibbs measure.

math-ph↗

arXiv2014

Weakly periodic Gibbs measures Of HC-model for normal divisor of the index four

In this paper is studied HC-model on a Cayley tree and under some conditions on parameters of the HC-model we prove existence of the weakly periodic (non periodic) Gibbs measures for normal divisor of the index four.

math-ph↗

arXiv2014

Translation-invariant Gibbs measures for the fertile HC-models with three states on a Cayley tree

We consider fertile HC-models with three states on a Cayley tree. It is known that four types of such models exist. For these models we describe the translation-invarinat Gibbs measures on a Cayley tree of order three.

math-ph↗

arXiv2014

New periodic Gibbs measures for Potts model with q-states on a Cayley tree

In this paper under some conditions on parameters of the Potts model with q-states on a Cayley tree of order k it is proved existence of the periodic (non translation-invariant)Gibbs measures. Also given a theorem about the number of these measures.

math-ph↗