22 citations · 70 across the 13 of their papers we have counts for
13 papers
Splitting Gibbs Measures for a Periodic Triple Mixed-Spin Ising Model on a Cayley Tree
Farrukh Mukhamedov, Muzaffar Rahmatullaev, Obid Karshiboev
We consider an Ising model on the Cayley tree of arbitrary order with three spin species of values distributed deterministically with period t…
A new set of Gibbs measures for the SOS model on a Cayley tree
Muzaffar M. Rahmatullaev, Bunyod U. Abraev
The phase transition phenomenon is one of the central problems of statistical mechanics. It occurs when the model possesses multiple Gibbs measures. In this paper, we consider a th…
The phase transition for the three-state SOS model with one-level competing interactions on the binary tree
Muzaffar M. Rahmatullaev, Obid Sh. Karshiboev
In this paper, we consider a three-state solid-on-solid (SOS) model with two competing interactions (nearest-neighbour, one-level next-nearest-neighbour) on the Cayley tree of orde…
Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree
M. M. Rahmatullaev, M. A. Rasulova, J. N Asqarov
We consider the Ising model with competing interactions and a nonzero external field on the Cayley tree of order two. We describe ground states and verify the Peierls condition for…
The Potts model on a Cayley tree: the new class of Gibbs measures
Muzaffar M. Rahmatullaev, Dekhkonov D. Jasur
For the Potts model on Cayley trees, a very wide class of new Gibbs measures is given. We give a review of all known Gibbs measures of the Potts model on trees and compare them wit…
Extremality of translation-invariant Gibbs measures for the Potts-SOS model on the Cayley tree
M. M. Rahmatullaev, M. A. Rasulova
In this paper, we consider the Potts-SOS model where the spin takes values in the set on the Cayley tree of order two. We describe all the translation-invariant split…