FUNKSIONAL EQUATIONS FOR THE LIMITING GIBBS MEASURES OF ISING-POTTS MODEL ON A CAYLEY TREE
DOI:
https://doi.org/10.52754/16948645_2024_1(4)_17Keywords:
Cayley tree, Ising-Potts model, periodic and weakly periodic ground statesAbstract
It is known that at low temperatures, each ground state corresponds to a Gibbs limit measure. Therefore, the task of studying the set of basic states for a given physical system is relevant. The Ising-Potts model on the Cayley tree is considered. In this paper, we study the ground state for the Ising-Potts model with three states on the Cayley tree. It is known that there exists a one-to-one correspondence between the set of the vertices of the Cayley tree of order and a group being a free product of cyclic groups of second order. We define periodic and weakly periodic ground states corresponding to normal divisors of the group . Periodic and weakly periodic ground states corresponding to the normal divisor of group are determined.
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