The Ising model on a Bethe lattice of order k ≥ 2 is considered. For maximum or minimum translation-invariant Gibbs states of this model, the relations between the von Neumann algebras generated by these states for the Gelfand-Neimark-Segal representation are found. These algebras can be of types IIIλ, λ ∈ (0, 1), and III1.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics