F. M. Mukhamedov, M. M. Rahmatullaev, M. A. Rasulova, “Extremality of translation-invariant Gibbs measures for the <nobr>$\lambda$</nobr>-model on the binary Cayley tree”, TMF, 2022, Volume 210, Number 3,Pages <nobr>470

This article is cited in 2 papers

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

F. M. Mukhamedov^ab, M. M. Rahmatullaev^bc, M. A. Rasulova^c

^a Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain, Abu Dhabi, United Arab Emirates
^b Romanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan
^c Namangan State University, Namangan, Uzbekistan

Abstract: 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.

Keywords: phase transition, extremality, Gibbs measure.

Received: 20.11.2021
Revised: 22.12.2021

DOI: 10.4213/tmf10206