Journal of Statistical Physics

, Volume 44, Issue 5–6, pp 713–728

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

  • George E. Andrews
  • R. J. Baxter
Articles

Abstract

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.

Key words

Statistical mechanics lattice statistics number theory hard hexagon model Rogers-Ramanujan identities 

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References

  1. 1.
    R. J. Baxter and G. E. Andrews,J. Stat. Phys. 44:249 (1986).Google Scholar
  2. 2.
    R. J. Baxter,J. Phys. A. 13:L61 (1980);J. Stat. Phys. 26:427 (1981).Google Scholar
  3. 3.
    L. J. Rogers,Proc. Lond. Math. Soc. 25:318 (1894).Google Scholar
  4. 4.
    S. Ramanujan,Proc. Camb. Phil. Soc. 19:214 (1919).Google Scholar
  5. 5.
    B. Gordon,Am. J. Math. 83:393 (1961).Google Scholar
  6. 6.
    A. Kuniba, Y. Akutsu, and M. Wadati,J. Phys. Soc. Japan. 55:1092, and to appear (1986).Google Scholar
  7. 7.
    G. E. Andrews, R. J. Baxter, and P. J. Forrester,J. Stat. Phys. 35:193 (1984).Google Scholar
  8. 8.
    G. E. Andrews,The Theory of Partitions (Addison-Wesley, Reading, Massachusetts, 1976).Google Scholar
  9. 9.
    R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic, London, 1982).Google Scholar
  10. 10.
    I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series and Products (Academic, New York, 1965).Google Scholar
  11. 11.
    D. A. Huse,Phys. Rev. B 30:3908 (1984).Google Scholar
  12. 12.
    D. A. Huse,Phys. Rev. Lett. 49:1121 (1982).Google Scholar
  13. 13.
    R. J. Baxter and P. A. Pearce,J. Phys. A 16:2239 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • George E. Andrews
    • 1
  • R. J. Baxter
    • 2
  1. 1.Department of Mathematics, McAllister BuildingPennsylvania State UniversityUniversity ParkUSA
  2. 2.Research School of Physical SciencesThe Australian National UniversityCanberraAustralia

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