Journal of Statistical Physics

, Volume 52, Issue 3–4, pp 639–667 | Cite as

Free energy of the solvable chiral Potts model

  • R. J. Baxter
Articles

Abstract

Very recently, it has been shown that there are chiralN-state Potts models in statistical mechanics that satisfy the star-triangle relation. Here it is shown that the relation implies that the free energy (and its derivatives) satisfies certain functional relations. These can be used to obtain the free energy: in particular, we expand about the critical case and find that the exponent α is 1−2/N.

Key words

Statistical mechanics lattice statistics Potts model 

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References

  1. 1.
    L. Onsager,Phys. Rev. 65:117 (1944).Google Scholar
  2. 2.
    R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).Google Scholar
  3. 3.
    H. Au-Yang, B. M. McCoy, J. H. H. Perk, and S. Tang, and M. L. Yan,Phys. Lett. A 123:219 (1987).Google Scholar
  4. 4.
    B. M. McCoy, J. H. H. Perk, S. Tang, and C. H. Sah,Phys. Lett. A 125:9 (1987).Google Scholar
  5. 5.
    R. J. Baxter, J. H. H. Perk, and H. Au-Yang,Phys. Lett. A 128:138 (1988).Google Scholar
  6. 6.
    Y. G. Stroganov,Phys. Lett. A 74:116 (1979).Google Scholar
  7. 7.
    R. J. Baxter, inFundamental Problems in Statistical Mechanics, Vol. 5, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1980).Google Scholar
  8. 8.
    R. J. Baxter,Physica 106A:18 (1981).Google Scholar
  9. 9.
    R. J. Baxter and I. G. Enting,J. Phys. 11:2463 (1978).Google Scholar
  10. 10.
    R. J. Baxter,Phil. Trans. R. Soc. 289:315 (1978).Google Scholar
  11. 11.
    R. J. Baxter,Proc. R. Soc. Lond. A 404:1 (1986).Google Scholar
  12. 12.
    R. J. Baxter,J. Stat. Phys. 28:1 (1982).Google Scholar
  13. 13.
    I. S. Gradshteyn and I. M. Ryzhik,Tables of Integrals, Series and Products (Academic Press, New York, 1965).Google Scholar
  14. 14.
    R. J. Baxter,J. Stat. Phys. 26:427 (1981).Google Scholar
  15. 15.
    V. A. Fateev and A. B. Zamolodchikov,Phys. Lett. 92A:37 (1982).Google Scholar
  16. 16.
    R. N. Onody and V. Kurak,J. Phys. A 17:L615 (1984).Google Scholar
  17. 17.
    M. Jumbo, T. Miwa, and M. Okado,Nucl. Phys. B 275:517 (1986).Google Scholar
  18. 18.
    A. B. Zamolodchikov and V. A. Fateev,Zh. Eksp. Teor. Fiz. 62:215 (1985).Google Scholar
  19. 19.
    A. B. Zamolodchikov and V. A. Fateev,Zh. Eksp. Teor. Fiz. 63:919 (1986).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • R. J. Baxter
    • 1
  1. 1.Research School of Physical SciencesAustralian National UniversityCanberraAustralia

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