Uniqueness for Gibbs measures of quantum lattices in small mass regime
Albeverio, Sergio ; Kondratiev, Yuri ; Kozitsky, Yuri ; Röckner, Michael
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001), p. 43-69 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2001-01-01
@article{AIHPB_2001__37_1_43_0,
     author = {Albeverio, Sergio and Kondratiev, Yuri and Kozitsky, Yuri and R\"ockner, Michael},
     title = {Uniqueness for Gibbs measures of quantum lattices in small mass regime},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {37},
     year = {2001},
     pages = {43-69},
     mrnumber = {1815773},
     zbl = {0980.60009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2001__37_1_43_0}
}

Albeverio, Sergio; Kondratiev, Yuri; Kozitsky, Yuri; Röckner, Michael. Uniqueness for Gibbs measures of quantum lattices in small mass regime. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) pp. 43-69. http://gdmltest.u-ga.fr/item/AIHPB_2001__37_1_43_0/

1 S Albeverio, R Høegh-Krohn, Homogeneous random fields and quantum statistical mechanics, J. Funct. Anal. Vol. 19 (1975) 242-272. | MR 378150 | Zbl 0381.60049

2 S Albeverio, R Høegh-Krohn, Mathematical Theory of Feynman Path Integrals, Lecture Notes in Math. 523, Springer, Berlin, 1976. | MR 495901 | Zbl 0337.28009

3 S Albeverio, Yu.G Kondratiev, Yu.V Kozitsky, Absence of critical points for a class of quantum hierarchical models, Comm. Math. Phys. Vol. 187 (1997) 1-18. | MR 1463820 | Zbl 0878.46046

4 S Albeverio, Yu.G Kondratiev, Yu.V Kozitsky, Suppression of critical fluctuations by strong quantum effects in quantum lattice systems, Comm. Math. Phys. Vol. 194 (1998) 493-512. | MR 1631465 | Zbl 0930.60088

5 Albeverio S., Kondratiev Yu.G., Kozitsky Yu.V., Röckner M., Euclidean Gibbs states of quantum lattice systems, in preparation. | Zbl 1029.82006

6 S Albeverio, Yu.G Kondratiev, R.A Minlos, A.L Rebenko, Small mass behaviour of quantum Gibbs states for lattice models with unbounded spins, J. Statist. Phys. Vol. 92 (1998) 1153-1172. | MR 1657797 | Zbl 0953.82005

7 S Albeverio, Yu.G Kondratiev, M Röckner, T.V Tsikalenko, Uniqueness of Gibbs states for quantum lattice systems, Probab. Theory Relat. Fields Vol. 108 (1997) 193-218. | MR 1452556 | Zbl 0883.60094

8 S Albeverio, Yu.G Kondratiev, M Röckner, T.V Tsikalenko, Uniqueness of Gibbs states on loop lattices, C. R. Acad. Sci. Paris, Sér. I Vol. 342 (1997) 1401-1406. | MR 1457095 | Zbl 0883.60093

9 S Albeverio, Yu.G Kondratiev, M Röckner, T.V Tsikalenko, Dobrushin's uniqueness for quantum lattice systems with nonlocal interaction, Comm. Math. Phys. Vol. 189 (1997) 621-630. | MR 1480036 | Zbl 0888.60094

10 Albeverio S., Kondratiev Yu.G., Röckner M., Tsikalenko T.V., Glauber dynamics for quantum lattice systems, Rev. Math. Phys., to appear. | MR 1813614 | Zbl 1081.82018

11 V.S Barbulyak, Yu.G Kondratiev, Functional integrals and quantum lattice systems: I. Existence of Gibbs states, Reports Nat. Acad. Sci. of Ukraine Vol. 9 (1991) 38-40.

12 V.S Barbulyak, Yu.G Kondratiev, Functional integrals and quantum lattice systems: II. Periodic Gibbs states, Reports Nat. Acad. Sci. of Ukraine Vol. 8 (1991) 31-34.

13 V.S Barbulyak, Yu.G Kondratiev, Functional integrals and quantum lattice systems: III. Phase transitions, Reports Nat. Acad. Sci. of Ukraine Vol. 10 (1991) 19-21. | MR 1153563

14 V.S Barbulyak, Yu.G Kondratiev, A criterion for the existence of periodic Gibbs states of quantum lattice systems, Selecta Math. (N.S.) Vol. 12 (1993) 25-35. | MR 1215524 | Zbl 0787.58046

15 F.A Berezin, M.A Shubin, The Schrödinger Equation, Kluwer Academic Publishers, Dordrecht, 1991. | MR 1186643 | Zbl 0749.35001

16 O Bratteli, D.W Robinson, Operator Algebras and Quantum Statistical Mechanics, I, II, Springer, New York, 1981. | MR 611508 | Zbl 0905.46046

17 A.D Bruce, R.A Cowley, Structural Phase Transition, Taylor and Francis, 1981.

18 R.L Dobrushin, Prescribing a system of random variables by conditional distributions, Theory Probab. Appl. Vol. 15 (1970) 458-486. | Zbl 0264.60037

19 R.L Dobrushin, S.B Shlosman, Constructive criterion for the uniqueness of Gibbs field, in: Statistical Physics and Dynamical Systems. Rigorous Results, Birkhäuser, Basel, 1985, pp. 347-370. | MR 821306 | Zbl 0569.46042

20 W Driesler, L Landau, J.F Perez, Estimates of critical lengths and critical temperatures for classical and quantum lattice systems, J. Statist. Phys. Vol. 20 (1979) 123-162. | MR 523638

21 F.J Dyson, E.H Lieb, B Simon, Phase transitions in quantum spin systems with isotropic and nonisotropic interactions, J. Statist. Phys. Vol. 18 (1978) 335-383. | MR 496246

22 H.O Georgii, Gibbs Measures and Phase Transition, Walter de Gruyter, Springer, Berlin, 1988. | MR 956646 | Zbl 0657.60122

23 S.A Globa, Yu.G Kondratiev, The construction of Gibbs states of quantum lattice systems, Selecta Math. Sov. Vol. 9 (1990) 297-307. | Zbl 0705.60102

24 F Guerra, L Rosen, B Simon, Boundary conditions in the P(ϕ)2 Euclidean field theory, Ann. Inst. H. Poincaré Vol. 15 (1976) 231-334. | Numdam

25 A Klein, L Landau, Stochastic processes associated with KMS states, J. Funct. Anal. Vol. 42 (1981) 368-428. | MR 626451 | Zbl 0498.60098

26 Yu.G Kondratiev, Phase transitions in quantum models of ferroelectrics, in: Stochastic Processes, Physics, and Geometry II, World Scientific, Singapore, 1994, pp. 465-475. | Zbl 0960.82536

27 Kozitsky Yu., Quantum effects in a lattice model of anharmonic vector oscillators, Letters in Math. Phys. (2000), to appear. | MR 1773204 | Zbl 1072.82512

28 H Künsch, Decay of correlations under Dobrushin's uniqueness condition and its applications, Comm. Math. Phys. Vol. 84 (1982) 207-222. | MR 661133 | Zbl 0495.60097

29 R.A Minlos, A Verbeure, V.A Zagrebnov, A quantum crystal model in the light mass limit Gibbs state, Preprint-KUL-TF-97/16, 1997.

30 L.A Pastur, B.A Khoruzhenko, Phase transitions in quantum models of rotators and ferroelectrics, Theoret. Math. Phys. Vol. 73 (1987) 111-124. | MR 939799

31 M Reed, B Simon, Methods of Modern Mathematical Physics. Functional Analysis, Vol. I, Academic Press, New York, 1972. | Zbl 0242.46001

32 T Schneider, H Beck, E Stoll, Quantum effects in an n-component vector model for structural phase transition, Phys. Rev. Vol. B13 (1976) 1123-1130.

33 B Simon, The P(ϕ)2 Euclidean (Quantum) Field Theory, Princeton Univ. Press, 1974.

34 B Simon, Functional Integrals in Quantum Physics, Academic Press, New York, 1986.

35 S Stamenković, Unified model description of order-disorder and displacive structural phase transitions, Condensed Matter Physics Vol. 1(14) (1998) 257-309.

36 A Verbeure, V.A Zagrebnov, No-Go theorem for quantum structural phase transition, J. Phys. A: Math. Gen. Vol. 28 (1995) 5415-5421. | MR 1364147 | Zbl 0871.46043