3 papers
math-ph2024
Alternative Gibbs measure for fertile three-state Hard-Core models on a Cayley tree
Rustamjon Khakimov, Muhtorjon Makhammadaliev, Kamola Umrzakova
We consider fertile three-state Hard-Core (HC) models with the activity parameter on a Cayley tree. It is known that there exist four types of such models: "wrench"\,, "wand"…
math-ph2023
Tranlation-invariant Gibbs measures for the Hard-Core model with a countable set of spin values
R. M. Khakimov, M. T. Makhammadaliev
In this paper, we study the Hard Core (HC) model with a countable set of spin values on a Cayley tree of order . This model is defined by a countable set of parame…
math.PR2023
New class of Gibbs measures for two state Hard-Core model on a Cayley tree
R. M. Khakimov, M T. Makhammadaliev, F. H. Haydarov
In this paper, we consider a Hard-Core model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance con…