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This article is cited in 11 scientific papers (total in 11 papers)
Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice
F. M. Mukhamedov Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
Abstract:
The Ising model on a Bethe lattice of order $k\geq2$ 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 $\mathrm{III}_\lambda$, $\lambda\in(0,1)$, and $\mathrm{III}_1$.
Received: 13.07.1999
Citation:
F. M. Mukhamedov, “Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice”, TMF, 123:1 (2000), 88–93; Theoret. and Math. Phys., 123:1 (2000), 489–493
Linking options:
https://www.mathnet.ru/eng/tmf588https://doi.org/10.4213/tmf588 https://www.mathnet.ru/eng/tmf/v123/i1/p88
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