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Coupled Ising-Potts Model: Rich Sets of Critical Temperatures and Translation-Invariant Gibbs Measures
F. H. Haydarov, B. A. Omirov, U. A. Rozikov
We consider a coupled Ising-Potts model on Cayley trees of order . This model involves spin vectors , and generalizes both the Ising and Potts models by incor…
Invariance property on group representations of the Cayley tree and its applications
U. A. Rozikov, F. H. Haydarov
In the present paper, we give a certain condition on subgroups of the group representation of the Cayley tree such that an invariance property holds. Except for the given condition…
Fixed points of Lyapunov integral operators and Gibbs measures
F. H. Haydarov
In this paper we shall consider the connections between Lyapunov integral operators and Gibbs measures for four competing interactions of models with uncountable (i.e. ) set…
On positive solutions of the homogeneous Hammerstein integral equation
Yu. Kh. Eshkabilov, F. H. Haydarov
In this paper the existence and uniqueness positive fixed points of the one nonlinear integral operator are discussed. We prove that existence finite positive solutions of the inte…
Periodic Gibbs Measures for Models with Uncountable Set of Spin Values on a Cayley Tree
U. A. Rozikov, F. H. Haydarov
We consider models with nearest-neighbor interactions and with the set of spin values, on a Cayley tree of order . We study periodic Gibbs measures of the model wi…
Non-uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree
Yu. Kh. Eshkabilov, F. H. Haydarov, U. A. Rozikov
In this paper we construct several models with nearest-neighbor interactions and with the set of spin values, on a Cayley tree of order . We prove that each of the…
Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree
Yu. Kh. Eshkabilov, F. H. Haydarov, U. A. Rozikov
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"…