arXiv subjects
Publications and source records attributed to G. I. Botirov.
In the present paper we continue the investigation from [1] and consider the SOS (solid-on-solid) model on the Cayley tree of order $k \geq 2$. In the ferromagnetic SOS case on the Cayley tree, we find three solutions to a class of period-4 height-periodic boundary law equations and these boundary laws define up to three periodic gradient Gibbs measures.
We consider Potts model, with competing interactions and countable spin values $Φ=\{0,1,\dots \}$ on a Cayley tree of order three. We study periodic ground states for this model.
We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. Recently, solving this integral equation some periodic (in particular translation-invariant) splitting Gibbs measures were found. In this paper we give three constructions of new sets of non-translation-invariant splitting Gibbs measures. Our constructions are based on known solutions of the integral equation.
In this paper we consider models with nearest-neighbor interactions and with the set [0,1] of spin values, on a Bethe lattice (Cayley tree) of an arbitrary order. These models depend on parameter $θ$. We describe all of Gibbs measures in any right parameter $θ$ corresponding to the models.
In this paper we consider a model with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k \geq 2$. To study translation-invariant Gibbs measures of the model we drive an nonlinear functional equation. For $k=2$ and 3 under some conditions on parameters of the model we prove non-uniqueness of translation-invariant Gibbs measures (i.e. there are phase transitions).
We consider the Potts model with two-step interactions and spin values 1,2,3,4 on a Cayley tree. We describe periodic ground states and verify the Peierls condition for the model.
In this paper we consider a model on a Cayley tree which has a finite radius of interactions, the model was first considered by Rozikov. We describe a set of periodic ground states of the model.
In the paper we generalize results of paper [12] for a $q$- component models on a Cayley tree of order $k\geq 2$. We generalize them in two directions: (1) from $k=2$ to any $k\geq 2;$ (2) from concrete examples (Potts and SOS models) of $q-$ component models to any $q$- component models (with nearest neighbor interactions). We give a set of periodic ground states for the model. Using the contour argument which was developed in [12] we show existence of $q$ different Gibbs measures for $q$-component models on Cayley tree of order $k\geq 2$.