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TMF, 2000, Volume 123, Number 1, Pages 88–93 (Mi tmf588)  

This article is cited in 9 scientific papers (total in 9 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 $\mathrm{III}_1$.

DOI: https://doi.org/10.4213/tmf588

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English version:
Theoretical and Mathematical Physics, 2000, 123:1, 489–493

Bibliographic databases:

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

Citation in format AMSBIB
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\paper Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice
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\jour Theoret. and Math. Phys.
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\vol 123
\issue 1
\pages 489--493
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mukhamedov F, Rozikov U, “On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras”, Journal of Statistical Physics, 114:3–4 (2004), 825–848  crossref  mathscinet  zmath  adsnasa  isi
    2. Mukhamedov, F, “On a factor associated with the unordered phase of lambda-model on a Cayley tree”, Reports on Mathematical Physics, 53:1 (2004), 1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Mukhamedov, F, “On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras II”, Journal of Statistical Physics, 119:1–2 (2005), 427  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Fidaleo F., Mukhamedov F., “On factors associated with quantum Markov states corresponding to nearest neighbor models on a Cayley tree”, Quantum Probability and Infinite Dimensional Analysis, Qp-Pq Quantum Probability and White Noise Analysis, 18, 2005, 237–251  crossref  mathscinet  isi
    5. L. Accardi, F. M. Mukhamedov, M. Kh. Saburov, “Uniqueness of Quantum Markov Chains Associated with an $XY$-Model on a Cayley Tree of Order $2$”, Math. Notes, 90:2 (2011), 162–174  mathnet  crossref  crossref  mathscinet  isi
    6. Mukhamedov F., Barhoumi A., Souissi A., “On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree”, Math. Phys. Anal. Geom., 19:4 (2016), 21  crossref  mathscinet  isi  elib  scopus
    7. Accardi L. Mukhamedov F. Souissi A., “On Construction of Quantum Markov Chains on Cayley trees”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, ed. Ayupov S. Chilin V. Ganikhodjaev N. Mukhamedov F. Rakhimov I., IOP Publishing Ltd, 2016, 012018  crossref  isi  scopus
    8. Mukhamedov F., Barhoumi A., Souissi Abdessatar, “Phase Transitions for Quantum Markov Chains Associated with Ising Type Models on a Cayley Tree”, J. Stat. Phys., 163:3 (2016), 544–567  crossref  mathscinet  zmath  isi  elib  scopus
    9. Mukhamedov F., Barhoumi A., Souissi A., El Gheteb S., “On Translation Invariant Quantum Markov Chains Associated With Ising-Xy Models on a Cayley Tree”, 37Th International Conference on Quantum Probability and Related Topics (Qp37), Journal of Physics Conference Series, 819, eds. Accardi L., Mukhamedov F., Hee P., IOP Publishing Ltd, 2017, UNSP 012006  crossref  mathscinet  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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