32 citations · 119 across the 23 of their papers we have counts for
23 papers
Infinite dimensional analogues of nilpotent and solvable Lie algebras
F. H. Haydarov, B. A. Omirov, G. O. Solijanova
We study infinite-dimensional analogues of nilpotent and solvable Lie algebras, focusing on the classes of pro-nilpotent, residually nilpotent, pro-solvable and residually solvable…
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…
Non-Gibbsian Multivariate Ewens Probability Distributions on Regular Trees
F. H. Haydarov, Z. E. Mustafoyeva, U. A. Rozikov
Ewens' sampling formula (ESF) provides the probability distribution governing the number of distinct genetic types and their respective frequencies at a selectively neutral locus u…
Gradient Gibbs measures with periodic boundary laws of a generalized SOS model on a Cayley tree
F. H. Haydarov, R. A. Ilyasova
We consider Gradient Gibbs measures corresponding to a periodic boundary law for a generalized SOS model with spin values from a countable set, on Cayley trees. On the Cayley tree,…
Gibbs measures on spatial systems on vertices of Cayley trees
F. H. Haydarov
There are many research works devoted to Gibbs measure for models on Cayley trees. Among these works, there are some works in which the general results are identical, but the consi…
New class of Gibbs measures for two state Hard-Core model on a Cayley tree
R. M. Khakimov, M T. Makhammadaliev, F. H. Haydarov
In this paper, we consider a Hard-Core model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance con…
Kolmogorov extension theorem for non-probability measures on Cayley trees
F. H. Haydarov
In this paper, we shall discuss the extendability of probability and non-probability measures on Cayley trees to a -additive measure on Borel fields which has a fundamental role…
A HC model with countable set of spin values: uncountable set of Gibbs measures
U. A. Rozikov, F. H. Haydarov
We consider a hard core (HC) model with a countable set of spin values on the Cayley tree. This model is defined by a countable set of parameters $λ_{i}>0, i \in \math…
Gradient Gibbs measures of a SOS model on Cayley trees: 4-periodic boundary laws
F. H. Haydarov, U. A. Rozikov
For SOS (solid-on-solid) model with external field and with spin values from the set of all integers, on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corres…
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…
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…
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…
Translation-invariant and periodic Gibbs measures for Potts model on a Cayley tree
R. M. Khakimov, F. H. Haydarov
In this paper is studied ferromagnetic three states Potts model on a Cayley tree of order three and we give explicit formulas for translation-invariant Gibbs measures. Furthermore,…
On the subgroups and normal subgroups of the group representation of the Cayley tree
F. H. Haydarov
In this paper, we give a characterization of the normal subgroups of index and of the subgroups of index three of the group representa…
Four Competing interactions for models with uncountable set of spin values on a Cayley Tree
U. A. Rozikov, F. H. Haydarov
In this paper we consider four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) of models with uncountable (i.e. ) set of…
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…
New normal subgroups for the group representation of the Cayley tree
F. H. Haydarov
In this paper we give full description of normal subgroups of index eight and ten for the group.
On three-state Potts model on a Cayley tree: periodic measures
F. H. Haydarov, R. M. Khakimov
In this paper we show that under some conditions on the parameter of the Potts model with three states with zero external field on the Cayley tree of order , there are exactly…
New Phase transitions of the Ising model on Cayley trees
D. Gandolfo, F. H. Haydarov, U. A. Rozikov +1
We show that the nearest neighbors Ising model on the Cayley tree exhibits new temperature driven phase transitions. These transitions holds at various inverse temperatures differe…
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"…