Journal of Statistical Physics

, Volume 33, Issue 1, pp 23–29 | Cite as

Phase transition in a lattice gas of hard spheres with second-neighbor exclusions on the simple cubic lattice

  • Dale A. Huckaby


Using reflection positivity and the Peierls argument, we prove the existence of an ordered phase at sufficiently high activity for a lattice gas of hard spheres on the simple cubic lattice with first- and second-neighbor exclusions.

Key words

Phase transitions lattice gas Peierls' argument reflection positivity 


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  1. 1.
    L. K. Runnels, inPhase Transitions and Critical Phenomena, Vol. II, C. Domb and M. Green, eds. (Academic, New York, 1972), p. 305.Google Scholar
  2. 2.
    R. L. Dobrushin,Funct. Anal. Appl. 2:292, 302 (1968).Google Scholar
  3. 3.
    O. J. Heilmann,Nuovo Cimento Lett. 3:95 (1972).Google Scholar
  4. 4.
    O. J. Heilmann,Commun. Math. Phys. 36:91 (1974).Google Scholar
  5. 5.
    L. K. Runnels,Commun. Math. Phys. 40:37 (1975).Google Scholar
  6. 6.
    O. J. Heilmann,J. Phys. A 13:1803 (1980).Google Scholar
  7. 7.
    R. J. Baxter,J. Phys. A 13:L61 (1980).Google Scholar
  8. 8.
    J. Orban and A. Bellemans,J. Chem. Phys. 49:363 (1968).Google Scholar
  9. 9.
    J. Orban,Chem. Phys. Lett. 3:702 (1969).Google Scholar
  10. 10.
    L. K. Runnels, J. R. Craig, and H. R. Streiffer,J. Chem. Phys. 54:1234 (1971).Google Scholar
  11. 11.
    A. Bellemans and R. K. Nigam,Phys. Rev. Lett. 16:1038 (1966).Google Scholar
  12. 12.
    B. R. Riemenschneider and D. A. Huckaby,J. Chem. Phys. 58:3940 (1973).Google Scholar
  13. 13.
    J. Orban,J. Phys. A 15:L501 (1982).Google Scholar
  14. 14.
    O. J. Heilmann and E. Praestgaard,J. Phys. A 7:1913 (1974).Google Scholar
  15. 15.
    O. J. Heilmann and E. Praestgaard,J. Stat. Phys. 9:23 (1973).Google Scholar
  16. 16.
    D. A. Huckaby,Phys. Rev. B 20:1208 (1979).Google Scholar
  17. 17.
    J. Fröhlich, R. B. Israel, E. H. Lieb, and B. Simon,J. Stat. Phys. 22:297 (1980).Google Scholar
  18. 18.
    O. J. Heilmann and E. H. Lieb,J. Stat. Phys. 20:679 (1979).Google Scholar
  19. 19.
    R. Peierls,Proc. Cambridge Philos. Soc. 32:477 (1936).Google Scholar
  20. 20.
    See, e.g., Ya. G. Sinai,Teoria Fazovyh Perekhodov (Russian) (Nauka, Moscow, 1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Dale A. Huckaby
    • 1
  1. 1.Department of ChemistryTexas Christian UniversityFort Worth

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