Skip to main content
Log in

Chiral Potts model as a descendant of the six-vertex model

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We observe that theN-state integrable chiral Potts model can be considered as a part of some new algebraic structure related to the six-vertex model. As a result, we obtain a functional equation which is supposed to determine all the eigenvalues of the chiral Potts model transfer matrix.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Onsager,Phys. Rev. 65:117 (1944).

    Google Scholar 

  2. R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).

    Google Scholar 

  3. L. D. Faddeev,Sov. Sci. Rev. C 1:107–155 (1980).

    Google Scholar 

  4. H. Au-Yang, B. M. McCoy, J. H. H. Perk, S. Tang, and M. Yan,Phys. Lett. A 123:219 (1987).

    Google Scholar 

  5. B. M. McCoy, J. H. H. Perk, S. Tang, and C. H. Sah,Phys. Lett. A 125:9 (1987).

    Google Scholar 

  6. H. Au-Yang, B. M. McCoy, J. H. H. Perk, and S. Tang,Algebraic Analysis, Vol. 1, M. Kashiwara and T. Kawai, eds (Academic Press, New York, 1988).

    Google Scholar 

  7. R. J. Baxter, J. H. H. Perk, and H. Au-Yang,Phys. Lett. A 128:138 (1988); H. Au-Yang and J. H. H. Perk, Onsager's star triangle equation: Master key to the integrability, inAdvanced Studies in Pure Mathematics, Vol. 19 (Kinokuniya-Academic, 1989).

    Google Scholar 

  8. L. Dolan and M. Grady,Phys. Rev. D 25:1587 (1982).

    Google Scholar 

  9. S. Howes, L. P. Kadanoff, and M. den Nijs,Nucl. Phys. B 215[FS7]:169 (1983).

    Google Scholar 

  10. G. von Gehlen and V. Rittenberg,Nucl. Phys. B 257[FS14]:351 (1985).

    Google Scholar 

  11. E. H. Lieb,Phys. Rev. 162:162 (1967);Phys. Lett. 18:1046,19:108 (1967).

    Google Scholar 

  12. B. Sutherland,Phys. Rev. Lett. 19:103 (1967).

    Google Scholar 

  13. G. Albertini, B. M. McCoy, and J. H. H. Perk, Eigenvalue spectrum of the superintegrable chiral Potts model,” inAdvanced Studies in Pure Mathematics, Vol. 19 (Kinokuniya-Academic, 1989).

  14. G. Albertini, B. M. McCoy, and J. H. H. Perk,Phys. Lett. A 139:204 (1989).

    Google Scholar 

  15. G. Albertini, B. M. McCoy, and J. H. H. Perk,Phys. Lett. A 135:159 (1989).

    Google Scholar 

  16. R. J. Baxter,Phys. Lett. A 133:185 (1988).

    Google Scholar 

  17. R. J. Baxter, A simple solvableZ n Hamiltonian,Phys. Lett. A, to appear.

  18. R. J. Baxter, Superintegrable chiral Potts models, thermodynamic properties, an “inverse” model, and a simple associated Hamiltonian, Preprint CMA-R12-89, Canberra (1989), to appear inJ. Stat. Phys.

  19. R. J. Baxter, V. V. Bazhanov, and J. H. H. Perk, Functional relations for transfer matrices of the chiral Potts model, in Proceedings of Australian National University Workshop on Yang-Baxter equations, Canberra (1989), to be published inInt. J. Mod. Phys. B.

  20. V. G. Drinfeld, “Quantum Groups,”Proc. Int. Congress of Mathematics, Berkeley, 1987, pp. 798–820.

  21. L. D. Faddeev, N. Yu. Reshetikhin, and L. A. Takhtajan,Algebra Analiz 1(1):178 (1989).

    Google Scholar 

  22. E. K. Sklyanin,Funk. Anal. Prilozh. 16(4):27 (1982).

    Google Scholar 

  23. V. A. Fateev and A. B. Zamolodchikov,Phys. Lett. A 92:37 (1982).

    Google Scholar 

  24. A. G. Izergin and V. E. Korepin,Nucl. Phys. B 205:401 (1982); V. O. Tarasov,Teor. Mat. Fiz. 63(2):175 (1985).

    Google Scholar 

  25. R. J. Baxter,Ann. Phys. 76:1 (1973).

    Google Scholar 

  26. V. B. Matveev and A. O. Smirnov, Some comments on the solvable chiral Potts model,Lett. Math. Phys. (1989).

  27. A. N. Kirillov and N. Y. Reshetikhin,J. Phys. A: Math. Gen. 19:565 (1986).

    Google Scholar 

  28. Y. E. Korepin and V. O. Tarasov. Private communication.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bazhanov, V.V., Stroganov, Y.G. Chiral Potts model as a descendant of the six-vertex model. J Stat Phys 59, 799–817 (1990). https://doi.org/10.1007/BF01025851

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01025851

Key words

Navigation