Geodesic
Uniqueness of states satisfying Kubo–Martin–Schwinger boundary conditions in the case of one-dimensional quantum spin systems with finite-range potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 1, pp. 120-130 
V. V. Anshelevich. Uniqueness of states satisfying Kubo–Martin–Schwinger boundary conditions in the case of one-dimensional quantum spin systems with finite-range potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 1, pp. 120-130. http://geodesic.mathdoc.fr/item/TMF_1972_13_1_a9/
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     title = {Uniqueness of states satisfying {Kubo{\textendash}Martin{\textendash}Schwinger} boundary conditions in the case of one-dimensional quantum spin systems with finite-range potential},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For one-dimensional quantum spin systems with finite-range potential Araki [1] has constructed a state that is the thermodynamic limit of Gibbs states in finite volumes and satisfies the Kubo–Martin–Schwinger boundary conditions. In the present paper it is shown that for the systems considered by Araki a state satisfying the Kubo–Martin–Schwinger boundary conditions is unique. This result means that all one-dimensional quantum spin systems with finite-range potential are single-phase.

[1] H. Araki, Commun. Math. Phys., 14 (1969), 120 | DOI | MR | Zbl

[2] R. Haag, N. M. Hugenholtz, M. Winnink, Commun. Math. Phys., 5 (1967), 215 | DOI | MR | Zbl

[3] H. J. Brascamp, Commun. Math. Phys., 18 (1970), 82 | DOI | MR

[4] R. L. Dobrushin, Funktsionalnyi analiz i ego prilozheniya, 3:1 (1969), 27 | MR | Zbl

[5] O. E. Landford, D. Ruelle, Commun. Math. Phys., 13 (1968), 194 | DOI | MR

[6] D. Ryuel, Statisticheskaya mekhanika. Strogie rezultaty, «Mir», 1971