$p$-Adic Hard Core models on a Cayley tree

In this talk, the $p$-adic Gibbs measures for the Hard Core (HC) models on a Cayley tree will be constructed. It will be found some conditions on parameters $k$ and prime number $p$, such that there is at least one $p$-adic Gibbs measure on a Cayley tree of order $k$. Moreover, for any prime number $p>2$, a description of the set of all translation-invariant $p$-adic Gibbs measures on a Cayley tree of order two will be given.