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The Potts model on a Cayley tree: the new class of Gibbs measures
Muzaffar M. Rahmatullaev, Dekhkonov D. Jasur
For the Potts model on Cayley trees, a very wide class of new Gibbs measures is given. We give a review of all known Gibbs measures of the Potts model on trees and compare them wit…
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 on the Cayley tree of order two. We describe all the translation-invariant split…
On Ground States and Phase Transition for -Model with the Competing Potts Interactions on Cayley Trees
Farrukh Mukhamedov, Chin Hee Pah, Hakim Jamil +1
In this paper, we consider the -model with nearest neighbor interactions and with competing Potts interactions on the Cayley tree of order-two. We notice that if -function is…
On a -Adic Generalized Gibbs Measure for Ising Model on a Cayley Tree
Muzaffar Rahmatullaev, Otabek Khakimov, Akbarxoja Tukhtaboev
In this paper we consider a -adic Ising model on the Cayley tree of order . We give full description of all -adic translation-invariant generalized Gibbs measures fo…
Weakly periodic Gibbs measures of the Ising model on the Cayley tree of order five and six
Nasir Ganikhodjaev, Muzaffar Rahmatullaev, Mohd Hirzie Bin Mohd Rodzhan
For Ising model on the Cayley tree of order five and six we present new weakly periodic (non-periodic) Gibbs measures corresponding to normal subgroups of indices two in the group…
Ising model on Cayley trees: a new class of Gibbs measures and their comparison with known ones
M. M. Rakhmatullaev, U. A. Rozikov
For the Ising model on Cayley trees we give a very wide class of new Gibbs measures. We show that these new measures are extreme under some conditions on the temperature. We give a…