A HC model with countable set of spin values: Uncountable set of Gibbs measures
U. A. RozikovAKFA University, 264, Milliy Bog Street, Yangiobod QFY, Barkamol MFY, Kibray District, 111221, Tashkent Region, UzbekistanF. H. HaydarovAKFA University, 264, Milliy Bog Street, Yangiobod QFY, Barkamol MFY, Kibray District, 111221, Tashkent Region, Uzbekistan
ABI
Аннотация
We consider a hard core (HC) model with a countable set [Formula: see text] of spin values on the Cayley tree. This model is defined by a countable set of parameters [Formula: see text]. For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the given model is either translation-invariant or periodic with period two. Moreover, we construct uncountable set of Gibbs measures for this HC model.
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