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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…