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Extremality of translation-invariant Gibbs measures for the $$\lambda$$-model on the binary Cayley tree

Farrukh MukhamedovRomanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, UzbekistanM. M. RahmatullaevRomanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, UzbekistanM. A. RasulovaNamangan State University, Namangan, Uzbekistan

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We consider the $$\lambda$$ -model on the Cayley tree of order $$k=2$$ . Under some conditions, we study translation-invariant Gibbs measures. Moreover, we investigate whether these Gibbs measures are extremal or nonextremal in the set of all Gibbs measures.

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