Gibbs measures for p-adic Hard-Core model with a countable set of spin values

In the talk we discuss generalized Gibbs measure (GGM) for p-adic Hard-Core (HC) model with a countable set of spin values on a Cayley tree of order $k \geq 2$. This model is defined by a countable set of p-adic parameters. We analyze p-adic functional equation which provides the consistency condition for the finite-dimensional generalized Gibbs distributions. Each solutions of the functional equation defines a GGM by p-adic version of Kolmogorov's theorem. Under some conditions on parameters of the model we give the number of translation-invariant and two-periodic GGMs for the p-adic HC model on the Cayley tree of order two.