Journal of Statistical Physics

, Volume 50, Issue 5–6, pp 1201–1220 | Cite as

The equilibrium thermodynamics of a spin-boson model

  • J. T. Lewis
  • G. A. Raggio


We consider the equilibrium thermodynamics of a Dicke-type model forN identical spins of arbitrary magnitude interacting linearly and homogeneously with a boson field in a volumeVN, in the limitN→∞,VN→∞, withN/VN=const. The system exhibits a second-order phase transition; complete information on the spin polarizations and their correlations is obtained. The proofs use a general result on the free energy of quantum spin systems based on the large deviation principle and the Berezin-Lieb inequalities.

Key words

Spins coupled to a boson field Dicke maser model second-order phase transition large deviations 


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  1. 1.
    R. H. Dicke,Phys. Rev. 93:99 (1954).Google Scholar
  2. 2.
    M. Tavis and F. W. Cummings,Phys. Rev. 170:379 (1968).Google Scholar
  3. 3.
    G. Scharf,Helv. Phys. Acta 43:806 (1970).Google Scholar
  4. 4.
    K. Hepp and E. H. Lieb,Ann. Phys. (N.Y.) 76:360 (1973).Google Scholar
  5. 5.
    K. Hepp and E. H. Lieb,Phys. Rev. A 8:2517 (1973).Google Scholar
  6. 6.
    N. N. Bogoljubov and V. N. Plechko,Physica A 82:163 (1976).Google Scholar
  7. 7.
    A. M. Kurbatov and D. P. Sankovich,Theor. Math. Phys. 42:258 (1980).Google Scholar
  8. 8.
    A. Klemm, V. A. Zagrebnov, and P. Ziesche,J. Phys. A 10:1987 (1977).Google Scholar
  9. 9.
    V. A. Zagrebnov,Z. Phys. B 55:75 (1984).Google Scholar
  10. 10.
    N. N. Bogoljubov, J. G. Brankov, V. A. Zagrebnov, A. M. Kurbatov, and N. S. Tonchev,Russian Math. Surveys 39:1 (1984).Google Scholar
  11. 11.
    M. Fannes, P. N. M. Sisson, A. Verbeure, and J. C. Wolfe,Ann. Phys. (N.Y.) 98:38 (1976).Google Scholar
  12. 12.
    M. Fannes, H. Spohn, and A. Verbeure,J. Math. Phys. 21:355 (1980).Google Scholar
  13. 13.
    W. Cegla, J. T. Lewis, and G. A. Raggio, The free energy of quantum spin systems and large deviations. Preprint, DIAS-STP 87-44. To appear inCommun. Math. Phys. Google Scholar
  14. 14.
    E. H. Lieb,Commun. Math. Phys. 31:327 (1973).Google Scholar
  15. 15.
    M. van den Berg, J. T. Lewis, and J. V. Pulè,Helv. Phys. Acta 59:1271 (1986).Google Scholar
  16. 16.
    J. M. Cook,J. Math. Phys. 2:33 (1961).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • J. T. Lewis
    • 1
  • G. A. Raggio
    • 1
  1. 1.Dublin Institute for Advanced StudiesDublin 4Ireland

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