Namangan State University

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20122024

most citedDescription of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree

86 citations

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math-ph2023★ 3 cited

Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree

M. M. Rahmatullaev, M. A. Rasulova, J. N Asqarov

We consider the Ising model with competing interactions and a nonzero external field on the Cayley tree of order two. We describe ground states and verify the Peierls condition for…

math-ph2022★ 2 cited

Gibbs measures for HC-model with a countable set of spin values on a Cayley tree

R. M. Khakimov, M. T. Makhammadaliev, U. A. Rozikov

In this paper, we study the HC-model with a countable set $Z$ of spin values on a Cayley tree of order $k \geq 2$ . This model is defined by a countable set of parameters (th…

math-ph2021★ 22 cited

Extremality of translation-invariant Gibbs measures for the Potts-SOS model on the Cayley tree

M. M. Rahmatullaev, M. A. Rasulova

In this paper, we consider the Potts-SOS model where the spin takes values in the set ${0, 1, 2}$ on the Cayley tree of order two. We describe all the translation-invariant split…

math-ph2019★ 11 cited

On Ground States and Phase Transition for $λ$ -Model with the Competing Potts Interactions on Cayley Trees

Farrukh Mukhamedov, Chin Hee Pah, Hakim Jamil +1

In this paper, we consider the $λ$ -model with nearest neighbor interactions and with competing Potts interactions on the Cayley tree of order-two. We notice that if $λ$ -function is…

math-ph2019★ 17 cited

On a $p$ -Adic Generalized Gibbs Measure for Ising Model on a Cayley Tree

Muzaffar Rahmatullaev, Otabek Khakimov, Akbarxoja Tukhtaboev

In this paper we consider a $p$ -adic Ising model on the Cayley tree of order $k \geq 2$ . We give full description of all $p$ -adic translation-invariant generalized Gibbs measures fo…

math-ph2017

Weakly periodic Gibbs measures for two and three state HC models on a Cayley tree

R. M. Khakimov, G. T. Madgoziyev

In this paper we study two and three state HC-model on a Cayley tree. Under some conditions on parameters of the HC-model, in the case of normal divisor of the index four, we prove…

math-ph2013★ 86 cited

Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree

C. Külske, U. A. Rozikov, R. M. Khakimov

For the $q$ -state Potts model on a Cayley tree of order $k \geq 2$ it is well-known that at sufficiently low temperatures there are at least $q + 1$ translation-invariant Gibbs measur…

math-ph2012★ 34 cited

On free energies of the Ising model on the Cayley tree

D. Gandolfo, M. M. Rakhmatullaev, U. A. Rozikov +1

We present, for the Ising model on the Cayley tree, some explicit formulae of the free energies (and entropies) according to boundary conditions (b.c.). They include translation-in…