Uniqueness of Gibbs states on loop lattices

Albeverio S, Kondratiev Y, Röckner M, Tsikalenko TV (1997)
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 324(12): 1401-1406.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We prove the uniqueness of Gibbs states for certain quantum lattice systems with unbounded spins, based on Dobrushin's fundamental uniqueness criterion. The necessary estimates for the Vasershtein distance between one-point conditional distributions, with boundary differing only at one site, are obtained from the Log-Sobolev inequality which holds on the infinite dimensional single spin (= loop) spaces. Detailed proofs are contained in [2] and [3]. The latter deals with the more general case of nonharmonic pair potentials with possibly infinite radius of interaction.
Erscheinungsjahr
Zeitschriftentitel
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
Band
324
Ausgabe
12
Seite(n)
1401-1406
ISSN
PUB-ID

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Albeverio S, Kondratiev Y, Röckner M, Tsikalenko TV. Uniqueness of Gibbs states on loop lattices. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE. 1997;324(12):1401-1406.
Albeverio, S., Kondratiev, Y., Röckner, M., & Tsikalenko, T. V. (1997). Uniqueness of Gibbs states on loop lattices. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 324(12), 1401-1406. doi:10.1016/S0764-4442(97)83583-5
Albeverio, S., Kondratiev, Y., Röckner, M., and Tsikalenko, T. V. (1997). Uniqueness of Gibbs states on loop lattices. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 324, 1401-1406.
Albeverio, S., et al., 1997. Uniqueness of Gibbs states on loop lattices. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 324(12), p 1401-1406.
S. Albeverio, et al., “Uniqueness of Gibbs states on loop lattices”, COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, vol. 324, 1997, pp. 1401-1406.
Albeverio, S., Kondratiev, Y., Röckner, M., Tsikalenko, T.V.: Uniqueness of Gibbs states on loop lattices. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE. 324, 1401-1406 (1997).
Albeverio, Sergio, Kondratiev, Yuri, Röckner, Michael, and Tsikalenko, Tatiana V. “Uniqueness of Gibbs states on loop lattices”. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 324.12 (1997): 1401-1406.