Dobrushin's uniqueness for quantum lattice systems with nonlocal interaction

Communications in Mathematical Physics

Volumn 189, Issue 2, 1997, Pages 621-630

  Albeverio, S ^a   Kondratiev, Yu G ^b,c   Rockner M ^b   Tsikalenko, T 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: 0031536799     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050220     Document Type: Article

References (34)

1. Albeverio, S., Høegh-Krohn, R.: Homogeneous random fields and quantum statistical mechanics. J. Funct. Anal. 19, 242-272 (1975)
2. Albeverio, S., Kondratiev, Yu.G., Röckner, M.: Dirichlet operators via stochastic analysis. J. Funct. Anal. 128, 102-138 (1995)
3. Albeverio, S., Kondratiev, Yu.G., Röckner, M., Tsikalenko, T.V.: Uniqueness of Gibbs states for quantum lattice systems. Probab. Th. Rel. Fields 108, 193-218 (1997)
4. Albeverio, S., Kondratiev, Yu.G., Röckner, M., Tsikalenko, T.V: Uniqueness of Gibbs states on loop lattices. C.R. Acad.Sci. 324,ser. 1. 1401-1406 (1997) Paris
5. Albeverio, S., Röckner, M.: Dirichlet forms on topological vector spaces - closability and a Cameron-Martin formula. J. Funct. Anal. 88, 395-436 (1990)
6. Barbulyak, V.S., Kondratiev, Yu.G.: The semiclassical limit for the Schrödinger operator and phase transitions in quantum statistical physics Funct. Anal. Appl., 26, 124 (1992)
7. Barbulyak, V.S., Kondratiev,: A criterion for the existence of periodic Gibbs states of quantum lattice systems. Selecta Math. Sov., 12, 25-35 (1993)
8. Bellissard, J., Høegh-Krohn, J.: Compactness and the maximal Gibbs states for random Gibbs fields on a lattice. Comm. Math. Phys. 84, 297-327 (1982)
9. Bellissard, J., Picco, J.: Lattice quantum fields: uniqueness and Markov property. Preprint Centre de Physique Theorique, Marseille (1978)
10. Cassandro, M., Olivieri, E., Pellegrinotti, A., Presutti, E.: Existence and uniqueness of DLR measures for unbounded spin systems. Z. Wahrsch. verw. Gebiete, 41, 313-334, (1978)
11. Deuschel, J.D., Stroock, D.W.: Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models. J.Funct.Anal 92, 30-48 (1990)
12. Dobrushin, R.L.: The description of a random field by means of conditional probabilities and conditions of its regularity. Theory Prob. Appl. 13, 197-224 (1968)
13. Dobrushin, R.L.: Prescribing a system of random variables by conditional distributions. Theory Prob. Appl., 15, 458-489 (1970)
14. Dobrushin, R.L., Shlosman, S.B.: Constructive criterion for the uniqueness of Gibbs field. In: Statistical Physics and Dynamical Systems. Rigorous results. Basel-Boston: Birkhäuser, 1985, pp. 347-370
15. Dobrushin, R.L., Shlosman, S.B., Kolafa, I.: Uniqueness of Gibbs random fields. Preprint IITP, Moscow (1986)
16. Föllmer, H.: A covariance estimate for Gibbs measures. J. Funct. Anal. 46, 387-395 (1982)
17. Georgii, H.O.: Gibbs measures and phase transitions. Studies in Mathematics 9, Berlin-New York: Walter de Gruyter, 1988
18. Globa, S.A., Kondratiev, Yu.G.: The construction of Gibbs states of quantum lattice systems. Selecta Math. Sov. 9, 297-307 (1990)
19. Gross, L.: Logarithmic Sobolev inequalities and contractivity properties of semigroups. In: Dirichlet forms, G.F. Dell'antonio et al. (eds.), Lecture Notes in Math. 1563, Berlin: Springer-Verlag, 1993
20. Klein, A., Landau, L.: Stochastic processes associated with KMS states. J. Funct. Anal. 42, 368-428 (1981)
21. Kondratiev, Yu.G.: Phase transitions in quantum models of ferroelectrics. In: Stochastic processes, physics and geometry II, Singapore - New Jersey: World Scientific, 1994 pp. 465-475
22. Künsch, H.: Decay of correlations under Dobrushin's uniqueness condition and its applications. Comm. Math. Phys. 84, 207-222 (1982)
23. Lebowitz, J.L., Presutti, E.: Statistical mechanics of systems of unbounded spins. Comm. Math. Phys. 50, 195-218 (1976)
24. Park, Y.M.: Quantum statistical mechanics of unbounded continuous spin systems. J. Korean Math. Soc. 22, 43-74 (1985)
25. Park, Y.M., Yoo, H.H.: A characterization of Gibbs states of lattice boson systems. J. Stat. Phys., 75, 215-239 (1994)
26. Park, Y.M., Yoo, H.H.: Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems. J. Stat. Phys., 80, 223-271 (1995)
27. Preston, C.: Random fields, Lecture Notes in Math. 534, Berlin: Springer-Verlag, 1976
28. Rachev, S.T.: Probability metrics and the stability of stochastic models. Wiley Series in Prob, and Math. Stat., Chichester-New York: Wiley, 1991
29. Rothaus, O.S.: Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities. J. Funct. Anal. 42, 102-109 (1981)
30. Royer, O.S.: Étude des champs Euclidiens sur un resau ℤv. J. Math. Pures et Appl. 56, 455-478 (1977)
31. Ruelle, D.: Probability estimates for continuous spin systems. Comm. Math. Phys. 50, 189-194 (1976)
32. Simon, B.: Functional integrals in quantum physics. New York: Academic Press, 1986
33. Stroock, D.W.: Logarithmic Sobolev inequalities for Gibbs states. In: Dirichlet forms, G. F. Dell'antonio et al. (eds.), Lect. Notes in Math. 1563, Berlin-Heidelberg-New York: Springer-Verlag, 1993
34. 2-convergence for infinite-dimensional reflecting diffusion processes. Science in China 38, 908-917 (1995)