Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice

F. M. Mukhamedov

doi:10.1007/BF02551055

Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice

F. M. Mukhamedov

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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 III_λ, λ ∈ (0, 1), and III₁.

Original language	English
Pages (from-to)	489-493
Number of pages	5
Journal	Theoretical and Mathematical Physics
Volume	123
Issue number	1
DOIs	https://doi.org/10.1007/BF02551055
Publication status	Published - Apr 2000
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02551055

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abstract = "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.",

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AB - 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.

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Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice

Abstract

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