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ArticleOriginal scientific text

Title

Quantum interfaces

Authors 1

Affiliations

  1. Department of Mathematics, University of California, Davis, Davis, California 95616-8633, U.S.A.

Abstract

We review recent results on interface states in quantum statistical mechanics.

Bibliography

  1. C. Borgs, J. Chayes and J. Fröhlich, Dobrushin states for classical spin systems with complex interactions, to appear in J. Stat. Phys.
  2. C. Borgs, J. Chayes and J. Fröhlich, Dobrushin states in quantum lattice systems, Commun. Math. Phys. 189 (1997), 591.
  3. O. Bratteli, A. Kishimoto and D. Robinson, Ground states of quantum spin systems, Commun. Math. Phys. 64 (1978), 41-48.
  4. O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics, 2 volumes, Springer Verlag-Berlin-Heidelberg-New York, 2nd edition, 1987 and 1996.
  5. R. L. Dobrushin, Gibbs states describing the coexistence of phases for a three-dimensional Ising model, Theor. Prob. Appl. 17 (1972), 582.
  6. N. Datta, A. Messager and B. Nachtergaele, Rigidity of interfaces in the Falicov-Kimball model, archived as math-ph/9804008.
  7. C.-T. Gottstein and R. F. Werner, Ground states of the infinite q-deformed Heisenberg ferromagnet, preprint archived as cond-mat/9501123.
  8. F. C. Alcaraz, S. R. Salinas and W. F. Wreszinski, Anisotropic ferromagnetic quantum domains, Phys. Rev. Lett. 75 (1995), 930.
  9. G. Albertini, V. E. Korepin and A. Schadschneider, XXZ model as an effective Hamiltonian for generalized Hubbard models with broken η-symmetry, J. Phys. A: Math. Gen. 25 (1995), L303-L309.
  10. T. Kennedy and E. H. Lieb, An itinerant electron model with crystalline or magnetic long-range order, Physica 138A (1986), 320-358.
  11. L. M. Falicov and J. C. Kimball, Phys. Rev. B 22 (1969), 997.
  12. M. Fannes and R. F. Werner, Boundary conditions for quantum lattice systems, Helv. Phys. Acta 68 (1995), 635-657.
  13. T. Matsui, On Ground States of the One-Dimensional Ferromagnetic XXZ Model, Lett. Math. Phys. 37 (1996), 397-403.
  14. T. Matsui, On the spectra of kink for ferromagnetic XXZ models, Lett. Math. Phys. 42 (1997), 229.
  15. T. Matsui, Translation Symmetry Breaking and Soliton Sectors for Massive Quantum Spin Models in 1+1 Dimensions, Commun. Math. Phys. 189 (1997), 127.
  16. A. Messager and S. Miracle-Solé, Low temperature states in the Falicov-Kimball model, Rev. Math. Phys. 8 (1996), 271.
  17. T. Koma and B. Nachtergaele, The spectral gap of the ferromagnetic XXZ chain, Lett. Math. Phys. 40 (1997), 1-16.
  18. T. Koma and B. Nachtergaele, The complete set of ground states of the ferromagnetic XXZ chains, preprint archived as cond-mat/9709208, to appear in Adv. Theor. Math. Phys.
  19. T. Koma and B. Nachtergaele, in preparation.
  20. A. W. Majewski and B. Zegarliński, Quantum Stochastic Dynamics I, Math. Phys. Electronic J. 1, No2 (1995), 37.
  21. A. W. Majewski, R. Olkiewicz and B. Zegarliński, this volume.
  22. J. Propp, private communication.
  23. R. H. Schonmann and S. B. Shlosman, Wulff droplets and the metastable relaxation of kinetic Ising models, archived as mparc # 97-272.
  24. B. Simon, The Statistical Mechanics of Lattice Gases, Vol 1, Princeton University Press, 1993.
Banach Center Publications
1998/43/1
Export to PBN, Opens in new tab
Pages:
321-329
Main language of publication
English
Published
1998
Exact and natural sciences