7 citations · 7 across the 8 of their papers we have counts for
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Gradient Gibbs measures for the SOS model with integer spin values on a Cayley tree
G. I. Botirov, F. H. Haydarov
In the present paper we continue the investigation from [1] and consider the SOS (solid-on-solid) model on the Cayley tree of order . In the ferromagnetic SOS case on the…
Non-translation-invariant Gibbs Measures for Models With Uncountable Set of Spin Values on a Cayley Tree
U. A. Rozikov, G. I. Botirov
We consider models with nearest-neighbor interactions and with the set of spin values, on a Cayley tree of order . It is known that the "splitting Gibbs measures"…
Phase transition for models with continuum set of spin values on Bethe lattice
Yu. Kh. Eshkabilov, G. I. Botirov, F. H. Haydarov
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 depe…
Phase Transitions for a model with uncountable set of spin values on a Cayley tree
Yu. Kh. Eshkabilov, U. A. Rozikov, G. I. Botirov
In this paper we consider a model with nearest-neighbor interactions and with the set of spin values, on a Cayley tree of order . To study translation-invariant G…
Ground States for Potts Model with Competing Interactions on Cayley Tree
G. I. Botirov
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.
On Ground States of Rozikov Model on the Cayley Tree
G. I. Botirov
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…