An extremality of the translation-invariant Gibbs measure for the HC-model on a Cayley tree

In this paper we study the extremality of translation-invariant Gibbs measure for the HC-model on a Cayley tree. It is known that for this model the translation-invariant measure is unique. We give a new proof of this statement and found regions of the extremality of this measure on the Cayley tree of order k.

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