Uniqueness of Gibbs states on loop lattices;Unicité des états de Gibbs sur des réseaux de lacets

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 324, Issue 12, 1997, Pages 1401-1406

  Albeverio, Sergio ^a   Kondratiev, Yuri G ^b,c   Röckner, Michael ^b   Tsikalenko, Tatiana V ^b,c  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b BIELEFELD UNIVERSITY   (Germany)

^c INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031161170     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(97)83583-5     Document Type: Article

References (9)

1. [1] Albeverio S. and Høegh-Krohn R., 1975. Homogeneous random fields and quantum statistical mechanics, J.Func.Anal., 19, pp. 242-272.
2. [2] Albeverio S., Kondratiev Yu. G., Röckner M. and TSikalenko T.V., 1996. Uniqueness of Gibbs states for quantum lattice systems, SFB 343, Preprint No. 96-022, Universität Bielefeld (to appear in Prob. Th. Rel. Fields).
3. [3] Albeverio S., Kondratiev Yu. G., Röckner M. and Tsikalenko T.V., 1996. Dobrushin's uniqueness for quantum lattice systems with nonlocal interaction, SFB/343 Preprint No. 96-078, Universität Bielefeld (to appear in Comm. Math. Phys.).
4. [4] Cassandro M., Olivieri E., Pellegrinotti A. and Presutti E., 1978. Existence and uniqueness of DLR measures for unbounded spin systems, Z. Wahrsch. verw. Gebiete, 41, pp. 313-334.
5. [5] Dobrushin R.L., 1970. Prescribing a system of random variables by conditional distributions, Theory Prob. Appl., 15, pp. 458-489.
6. [6] Föllmer H., 1982. A covariance estimate for Gibbs measures, J. Funct. Anal. 46, pp. 387-395.
7. [7] Georgii H.O., 1988. Gibbs measures and phase transitions, Studies in Mathematics, 9, Walter de Gruyter, Berlin-New York.
8. [8] Park Y.M. and Yoo H. H., 1994. A characterization of Gibbs states of lattice boson systems, J. Stat. Phys., 75, pp. 215-239.
9. [9] Park Y.M. and Yoo H. H., 1995. Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems, J. Stat. Phys., 80, pp. 223-271.