Uniqueness for Gibbs measures of quantum lattices in small mass regime

 Access to full text

 Full (PDF)

1. 1 S Albeverio, R Høegh-Krohn, Homogeneous random fields and quantum statistical mechanics, J. Funct. Anal.Vol. 19 (1975) 242-272. Zbl0381.60049MR378150
2. 2 S Albeverio, R Høegh-Krohn, Mathematical Theory of Feynman Path Integrals, Lecture Notes in Math. 523, Springer, Berlin, 1976. Zbl0337.28009MR495901
3. 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. Zbl0878.46046MR1463820
4. 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. Zbl0930.60088MR1631465
5. 5 Albeverio S., Kondratiev Yu.G., Kozitsky Yu.V., Röckner M., Euclidean Gibbs states of quantum lattice systems, in preparation. Zbl1029.82006
6. 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. Zbl0953.82005MR1657797
7. 7 S Albeverio, Yu.G Kondratiev, M Röckner, T.V Tsikalenko, Uniqueness of Gibbs states for quantum lattice systems, Probab. Theory Relat. FieldsVol. 108 (1997) 193-218. Zbl0883.60094MR1452556
8. 8 S Albeverio, Yu.G Kondratiev, M Röckner, T.V Tsikalenko, Uniqueness of Gibbs states on loop lattices, C. R. Acad. Sci. Paris, Sér. IVol. 342 (1997) 1401-1406. Zbl0883.60093MR1457095
9. 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. Zbl0888.60094MR1480036
10. 10 Albeverio S., Kondratiev Yu.G., Röckner M., Tsikalenko T.V., Glauber dynamics for quantum lattice systems, Rev. Math. Phys., to appear. Zbl1081.82018MR1813614
11. 11 V.S Barbulyak, Yu.G Kondratiev, Functional integrals and quantum lattice systems: I. Existence of Gibbs states, Reports Nat. Acad. Sci. of UkraineVol. 9 (1991) 38-40. 
12. 12 V.S Barbulyak, Yu.G Kondratiev, Functional integrals and quantum lattice systems: II. Periodic Gibbs states, Reports Nat. Acad. Sci. of UkraineVol. 8 (1991) 31-34. 
13. 13 V.S Barbulyak, Yu.G Kondratiev, Functional integrals and quantum lattice systems: III. Phase transitions, Reports Nat. Acad. Sci. of UkraineVol. 10 (1991) 19-21. MR1153563
14. 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. Zbl0787.58046MR1215524
15. 15 F.A Berezin, M.A Shubin, The Schrödinger Equation, Kluwer Academic Publishers, Dordrecht, 1991. Zbl0749.35001MR1186643
16. 16 O Bratteli, D.W Robinson, Operator Algebras and Quantum Statistical Mechanics, I, II, Springer, New York, 1981. Zbl0905.46046MR611508
17. 17 A.D Bruce, R.A Cowley, Structural Phase Transition, Taylor and Francis, 1981. 
18. 18 R.L Dobrushin, Prescribing a system of random variables by conditional distributions, Theory Probab. Appl.Vol. 15 (1970) 458-486. Zbl0264.60037
19. 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. Zbl0569.46042MR821306
20. 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. MR523638
21. 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. MR496246
22. 22 H.O Georgii, Gibbs Measures and Phase Transition, Walter de Gruyter, Springer, Berlin, 1988. Zbl0657.60122MR956646
23. 23 S.A Globa, Yu.G Kondratiev, The construction of Gibbs states of quantum lattice systems, Selecta Math. Sov.Vol. 9 (1990) 297-307. Zbl0705.60102
24. 24 F Guerra, L Rosen, B Simon, Boundary conditions in the P(ϕ)2 Euclidean field theory, Ann. Inst. H. PoincaréVol. 15 (1976) 231-334. 
25. 25 A Klein, L Landau, Stochastic processes associated with KMS states, J. Funct. Anal.Vol. 42 (1981) 368-428. Zbl0498.60098MR626451
26. 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. Zbl0960.82536
27. 27 Kozitsky Yu., Quantum effects in a lattice model of anharmonic vector oscillators, Letters in Math. Phys. (2000), to appear. Zbl1072.82512MR1773204
28. 28 H Künsch, Decay of correlations under Dobrushin's uniqueness condition and its applications, Comm. Math. Phys.Vol. 84 (1982) 207-222. Zbl0495.60097MR661133
29. 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. Zbl0976.82010
30. 30 L.A Pastur, B.A Khoruzhenko, Phase transitions in quantum models of rotators and ferroelectrics, Theoret. Math. Phys.Vol. 73 (1987) 111-124. MR939799
31. 31 M Reed, B Simon, Methods of Modern Mathematical Physics. Functional Analysis, Vol. I, Academic Press, New York, 1972. Zbl0242.46001
32. 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. 33 B Simon, The P(ϕ)2 Euclidean (Quantum) Field Theory, Princeton Univ. Press, 1974. 
34. 34 B Simon, Functional Integrals in Quantum Physics, Academic Press, New York, 1986. 
35. 35 S Stamenković, Unified model description of order-disorder and displacive structural phase transitions, Condensed Matter PhysicsVol. 1(14) (1998) 257-309. 
36. 36 A Verbeure, V.A Zagrebnov, No–Go theorem for quantum structural phase transition, J. Phys. A: Math. Gen.Vol. 28 (1995) 5415-5421. Zbl0871.46043MR1364147