Abstract
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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