On Gibbs Measures of Models with Competing Ternary and Binary Interactions and Corresponding Von Neumann Algebras II

Farruh Mukhamedov, Utkir Rozikov
2005 Journal of statistical physics  
In the present paper the Ising model with competing binary (J) and binary (J_1) interactions with spin values ± 1, on a Cayley tree of order 2 is considered. The structure of Gibbs measures for the model considered is studied. We completely describe the set of all periodic Gibbs measures for the model with respect to any normal subgroup of finite index of a group representation of the Cayley tree. Types of von Neumann algebras, generated by GNS-representation associated with diagonal states
more » ... esponding to the translation invariant Gibbs measures, are determined. It is proved that the factors associated with minimal and maximal Gibbs states are isomorphic, and if they are of type III_λ then the factor associated with the unordered phase of the model can be considered as a subfactors of these factors respectively. Some concrete examples of factors are given too. Keywords: Cayley tree, Ising model, competing interactions, Gibbs measure, GNS-construction, Hamiltonian, von Neumann algebra.
doi:10.1007/s10955-004-2056-3 fatcat:2em44cpgwjfspl6vcsnhtq3pny