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

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Abstract

The Ising model on a Bethe lattice of orderk≥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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Authors and Affiliations

  1. Romanovskii Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan

    F. M. Mukhamedov

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  1. F. M. Mukhamedov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 88–93, April, 2000.

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Mukhamedov, F.M. Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice. Theor Math Phys 123, 489–493 (2000). https://doi.org/10.1007/BF02551055

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