Journal of Statistical Physics

, Volume 17, Issue 5, pp 289–300 | Cite as

The Gaussian inequality for multicomponent rotators

  • J. Bricmont


The Gaussian inequality is proven for multicomponent rotators with negative correlations between two spin components. In the case of one-component systems, the Gaussian inequality is shown to be a consequence of Lebowitz' inequality. For multicomponent models, the Gaussian inequality implies that the decay rate of the truncated correlation (or Schwinger) functions is dominated by that of the two-point function. Applied to field theory, these inequalities give information on the absence of bound states in the λ(φ12 + φ12)2 model.

Key words

Classical rotators correlation inequalities 


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  1. 1.
    J. Bricmont, J. R. Fontaine, and L. J. Landau, On the Uniqueness of the Equilibrium State in Plane Rotators, Preprint.Google Scholar
  2. 2.
    F. Dunlop,Comm. Math. Phys. 49:247 (1976).Google Scholar
  3. 3.
    F. Dunlop and C. M. Newman,Comm. Math. Phys. 44:223 (1974).Google Scholar
  4. 4.
    R. S. Ellis, J. L. Monroe, and C. M. Newman,Comm. Math. Phys. 46:167 (1976).Google Scholar
  5. 5.
    R. S. Ellis and C. M. Newman,J. Math. Phys. 17:1682 (1976).Google Scholar
  6. 6.
    J. Feldman,Can. J. Phys. 52:1583 (1974).Google Scholar
  7. 7.
    J. Ginibre,Comm. Math. Phys. 16:310 (1970).Google Scholar
  8. 8.
    J. Glimm and A. Jaffe,Ann. Inst. H. Poincaré 22:1 (1975).Google Scholar
  9. 9.
    J. Glimm and A. Jaffe, A Tutorial Course in Constructive Field Theory, inProc. of the 1976 Cargèse Summer School, to appear.Google Scholar
  10. 10.
    J. Glimm and A. Jaffe,Phys. Rev. Lett. 33:440 (1974).Google Scholar
  11. 11.
    R. B. Griffiths, C. A. Hurst, and S. Sherman,J. Math. Phys. 11:790 (1970).Google Scholar
  12. 12.
    B. Simon and R. B. Griffiths,Comm. Math. Phys. 33:145 (1973).Google Scholar
  13. 13.
    H. Kunz, Ch. Ed. Pfister, and P. A. Vuillermot, Inequalities for Some Classical Spin Vector Models, Preprint.Google Scholar
  14. 14.
    J. L. Lebowitz,Comm. Math. Phys. 35:87 (1974).Google Scholar
  15. 15.
    J. L. Lebowitz,Comm. Math. Phys. 28:313 (1972).Google Scholar
  16. 16.
    O. A. Mac Bryan and T. Spencer,Comm. Math. Phys. 53:299 (1977).Google Scholar
  17. 17.
    J. L. Monroe,J. Math. Phys. 16:1809 (1975).Google Scholar
  18. 18.
    C. M. Newman, Gaussian Correlation Inequalities for Ferromagnets,Z. Wahrscheinlichkeitstheorie 33:75 (1975/76).Google Scholar
  19. 19.
    C. M. Newman,J. Math. Phys. 16:1956 (1975).Google Scholar
  20. 20.
    B. Simon,Comm. Math. Phys. 31:127 (1973).Google Scholar
  21. 21.
    B. Simon,The P(φ) 2 Euclidean (Quantum) Field Theory (Princeton University Press, 1974).Google Scholar
  22. 22.
    T. Spencer,Comm. Math. Phys. 39:77 (1974).Google Scholar
  23. 23.
    G. S. Sylvester, Continuous-Spin Inequalities for Ising Ferromagnets, Preprint.Google Scholar
  24. 24.
    G. S. Sylvester,Comm. Math. Phys. 42:209 (1975).Google Scholar
  25. 25.
    F. Dunlop, Zeros of Partition Function via Correlation Inequalities; Preprint, and other publication to appear.Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • J. Bricmont
    • 1
  1. 1.Institut de Physique ThéoriqueUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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