Geodesic
Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 1, pp. 88-93

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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 $\mathrm{III}_1$. 
@article{TMF_2000_123_1_a7,
     author = {F. M. Mukhamedov},
     title = {Von {Neumann} algebras generated by translation-invariant {Gibbs} states of the {Ising} model on a {Bethe} lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {88--93},
     publisher = {mathdoc},
     volume = {123},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_1_a7/}
}
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F. M. Mukhamedov. Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 1, pp. 88-93. http://geodesic.mathdoc.fr/item/TMF_2000_123_1_a7/