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- Title
(k<sub>0</sub><sup>(m)</sup>)-periodic Gibbs measures for the fertile three-state Hard-Core model in the case Wand.
- Authors
A., Bozorqulov
- Abstract
We consider fertile three-state Hard-Core (HC) models with the activity parameter λ > 0 on a Cayley tree. It is known that there exist four types of such models: wrench, wand, hinge, and pipe. We study (k0(m))-periodic Gibbs measures for the considered model in the case wand on the Cayley tree. Such measures are constructed by means of periodic Gibbs measures. In the case wand on the Cayley tree of order k = 3, 4 for k0 = 2 and m = 1 the existence of one (k0(m))-periodic Gibbs measure proved. Moreover, conditions for the existence and non-uniqueness of (k0(m))-periodic Gibbs measures on the Cayley tree of order k = 5 were found.
- Subjects
HINGES; WRENCHES; TREES; MEASUREMENT
- Publication
Uzbek Mathematical Journal, 2024, Vol 68, Issue 1, p42
- ISSN
2010-7269
- Publication type
Article
- DOI
10.29229/uzmj.2024-2-5