Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model
Р. М. ХакимовNamangan Department, Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Namangan, UzbekistanM. T. MakhammadalievNamangan State University, Namangam, Uzbekistan
ABI
Abstract
We study a “hard-core” model on a Cayley tree. In the case of a normal divisor of index 4, we show the uniqueness of weakly periodic Gibbs measures under certain conditions on the parameters. Moreover, we prove that there exist weakly periodic (nonperiodic) Gibbs measures different from those previously known.