Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand

Аннотация

We consider fertile three-state Hard-Core (HC) models with the activity parameter > 0 on a Cayley tree.It is known that there exist four types of such models: wrench, wand, hinge, and pipe.These models arise as simple examples of loss networks with nearest-neighbor exclusion.In the case wand on a Cayley tree of order k 2, exact critical values > 0 are found for which two-periodic Gibbs measures are not unique.Moreover, we study the extremality of the existing two-periodic Gibbs measures on a Cayley tree of order two.

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DOI

10.15407/mag20.01.066

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