Gibbs measures on Cayley trees: results and open problems
UA Rozikov - Reviews in Mathematical Physics, 2013 - World Scientific
The purpose of this review paper is to present systematically all known results on Gibbs
measures on Cayley trees (Bethe lattices). There are about 150 papers which contain …
measures on Cayley trees (Bethe lattices). There are about 150 papers which contain …
On the three state Potts model with competing interactions on the Bethe lattice
N Ganikhodjaev, F Mukhamedov… - Journal of Statistical …, 2006 - iopscience.iop.org
In the present paper the three state Potts model with competing binary interactions (with
couplings J and J p) on the second order Bethe lattice is considered. The recurrent …
couplings J and J p) on the second order Bethe lattice is considered. The recurrent …
Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree
The main aim of the present paper is to prove the existence of a phase transition in quantum
Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind …
Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind …
Refinement of quantum Markov states on trees
F Mukhamedov, A Souissi - Journal of Statistical Mechanics …, 2021 - iopscience.iop.org
In the present paper, we propose a refinement for the notion of quantum Markov states
(QMS) on trees. A structure theorem for QMS on general trees is proved. We notice that any …
(QMS) on trees. A structure theorem for QMS on general trees is proved. We notice that any …
On an algebraic property of the disordered phase of the Ising model with competing interactions on a Cayley tree
It is known that the disordered phase of the classical Ising model on the Caley tree is
extreme in some region of the temperature. If one considers the Ising model with competing …
extreme in some region of the temperature. If one considers the Ising model with competing …
On Quantum Markov Chains on Cayley Tree II: Phase Transitions for the Associated Chain with XY-Model on the Cayley Tree of Order Three
L Accardi, F Mukhamedov, M Saburov - Annales Henri Poincaré, 2011 - Springer
In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley
tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on …
tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on …
Extremality of Disordered Phase of λ-Model on Cayley Trees
F Mukhamedov - Algorithms, 2022 - mdpi.com
In this paper, we consider the λ-model for an arbitrary-order Cayley tree that has a
disordered phase. Such a phase corresponds to a splitting Gibbs measure with free …
disordered phase. Such a phase corresponds to a splitting Gibbs measure with free …
On S-Evolution Algebras and Their Enveloping Algebras
F Mukhamedov, I Qaralleh - Mathematics, 2021 - mdpi.com
In the present paper, we introduce S-evolution algebras and investigate their solvability,
simplicity, and semisimplicity. The structure of enveloping algebras has been carried out …
simplicity, and semisimplicity. The structure of enveloping algebras has been carried out …
On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
L Accardi, F Mukhamedov, M Saburov - … , Quantum Probability and …, 2011 - World Scientific
In this paper we study forward quantum Markov chains (QMC) defined on Cayley tree. A
construction of such QMC is provided, namely we construct states on finite volumes with …
construction of such QMC is provided, namely we construct states on finite volumes with …
Diagonalizability of quantum Markov states on trees
F Mukhamedov, A Souissi - Journal of Statistical Physics, 2021 - Springer
We introduce quantum Markov states (QMS) in a general tree graph G=(V, E) G=(V, E),
extending the Cayley tree's case. We investigate the Markov property wrt the finer structure …
extending the Cayley tree's case. We investigate the Markov property wrt the finer structure …