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Links between decay properties of correlations and analyticity of the pressure and correlation functions

  • Bernard Souillard
Session 62
Part of the Lecture Notes in Physics book series (LNP, volume 39)

Abstract

I will present here some results obtained in collaboration with Michel Duneau and Daniel Iagolnitzer.

Rigorous results on “strong clustering” of the correlations are indicated here and precise links between decay properties of correlations and analyticity properties of the pressure and correlation functions are exhibited.

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References

  1. [1]
    Onsager, L., Phys. Rev. 65, 117 (1944).CrossRefGoogle Scholar
  2. [2]
    Lebowitz, J. L.and Penrose, O., Commun. Math. Phys. 11, 99 (1968).CrossRefGoogle Scholar
  3. [3]
    Gallavotti, G. and Miracle-Sole, S. Commun. Math. Phys. 12, 269 (1969).CrossRefGoogle Scholar
  4. [4]
    Duneau, M., Iagolnitzer, D., and Souillard, B., Commun. Math. Phys. 31, 191 (1973).CrossRefGoogle Scholar
  5. [5]
    Duneau, M., Iagolnitzer, D., and Souillard, B., Commun. Math. Phys. 35, 307 (1974).CrossRefGoogle Scholar
  6. [5]a
    .Duneau, M., Iagolnitzer, D., and Souillard, B., Decay of correlations for infinite-range interactions, to be published in J. Math. Phys.(1975).Google Scholar
  7. [6]
    This method has first been used in ref. [2], [3] and has been adapted in ref. [5] to the proof of S.C.P.Google Scholar
  8. [7]
    Lebowitz, J.L. and Penrose, O.,: Phys. Rev. Letters 31, 749 (1973).CrossRefGoogle Scholar
  9. [7]a
    .Lebowitz, J.L. and Penrose, O.,: Commun. Math. Phys. 39, 165 (1974).CrossRefGoogle Scholar
  10. [8]
    Lieb, E.H. and Ruelle, D., J. Math. Phys. 13, 781 (1972).CrossRefGoogle Scholar
  11. [8]a
    .Ruelle, D., Commun. Math. Phys. 31, 265 (1973).CrossRefGoogle Scholar
  12. [9]
    Lebowitz, J.L., Commun. Math. Phys. 28, 313 (1972).CrossRefGoogle Scholar
  13. [10]
    Abraham, D. and Martin-Löf, A., Comm. Math. Phys. 32, 245 (1973).CrossRefGoogle Scholar
  14. [11]
    Ref. [4] and Duneau, M., Souillard, B., to be published.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Bernard Souillard
    • 1
  1. 1.Centre de Physique Théorique de l'Ecole PolytechniquePalaiseauFrance

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