Journal of Statistical Physics

, Volume 56, Issue 5–6, pp 965–972 | Cite as

A remark on different norms and analyticity for many-particle interactions

  • A. C. D. van Enter
  • R. Fernández
Short Communications


We compare a recent result of Dobrushin and Martirosyan with previous results by Gallavotti and Miracle-Sole and by Israel and point out that the analytic behavior at high temperatures for many-particle interactions is different depending on whether the interactions are weighted with a lattice-gas or Ising norm or, on the other hand, with the supremum norm.

Key words

Many-particle interactions physically equivalent interactions inequivalent norms analyticity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. L. Dobrushin and D. R. Martirosyan,Theor. Math. Phys. 75:443 (1988).Google Scholar
  2. 2.
    R. L. Dobrushin and D. R. Martirosyan,Theor. Math. Phys. 74:16 (1988).Google Scholar
  3. 3.
    G. Gallavotti and S. Miracle-Sole,Commun. Math. Phys. 7:274 (1968).Google Scholar
  4. 4.
    G. Gallavotti, S. Miracle-Sole, and D. W. Robinson,Phys. Lett. 25A:493 (1967).Google Scholar
  5. 5.
    R. B. Israel,Commun. Math. Phys. 50:245 (1976).Google Scholar
  6. 6.
    R. B. Israel,Convexity in the Theory of Lattice Gases (Princeton University Press, Princeton, New Jersey, 1979), especially Sections I.4 and III.4.Google Scholar
  7. 7.
    L. Gross,Commun. Math. Phys. 68:9 (1979).Google Scholar
  8. 8.
    L. Gross,J. Stat. Phys. 25:27 (1981).Google Scholar
  9. 9.
    L. Gross, inLecture Notes in Mathematics, No. 925 (Springer-Verlag, Berlin, 1982).Google Scholar
  10. 10.
    C. Prakash,J. Stat. Phys. 31:169 (1983).Google Scholar
  11. 11.
    O. Bratteli and D. W. Robinson,Operator Algebras and Quantum Statistical Mechanics, Vol. II (Springer-Verlag, Berlin, 1981).Google Scholar
  12. 12.
    Y. M. Park,J. Stat. Phys. 27:553 (1982).Google Scholar
  13. 13.
    W. Greenberg,Commun. Math. Phys. 11:314 (1968).Google Scholar
  14. 14.
    W. Greenberg,Commun. Math. Phys. 13:335 (1969).Google Scholar
  15. 15.
    O. E. Lanford, inCargèse Lectures in Physics, Vol. 4, D. Kastler, ed. (Gordon and Breach, New York, 1970).Google Scholar
  16. 16.
    D. Ruelle,Thermodynamic Formalism (Addison-Wesley, New York, 1978), Chapter 4.7.Google Scholar
  17. 17.
    N. M. Hugenholtz, inProceedings Symposium Pure Mathematics, Vol. 38 (American Mathematical Society, Providence, Rhode Island, 1982), Part 2, pp. 407–465, § 7.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • A. C. D. van Enter
    • 1
  • R. Fernández
    • 1
  1. 1.Department of MathematicsUniversity of Texas at AustinAustin

Personalised recommendations