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Functional Relations for the Order Parameters of the Chiral Potts Model

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Following the method of Jimbo, Miwa, and others, we obtain functional relations for the order parameters of the chiral Potts model. We have not yet solved these relations. Here we discuss their properties and show how one should beware of spurious solutions.

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REFERENCES

  1. L. Dolan and M. Grady, Phys. Rev. D 25:1587–1604 (1982).

    Google Scholar 

  2. S. Howes, L. P. Kadanoff, and M. den Nijs, Nucl. Phys. B 215[FS7]:169–208 (1983).

    Google Scholar 

  3. G. von Gehlen and V. Rittenberg, Nucl. Phys. B 257[FS14]:351–370 (1985).

    Google Scholar 

  4. H. Au-Yang, B. M. McCoy, J. H. H. Perk, S. Tang, and M.-L. Yan, Phys. Lett. A 123:219–223 (1987).

    Google Scholar 

  5. B. M. McCoy, J. H. H. Perk, and S. Tang, Phys. Lett. A 125:9–14 (1987).

    Google Scholar 

  6. R. J. Baxter, J. H. H. Perk, and H. Au-Yang, Phys. Lett. A 128:138–142 (1988).

    Google Scholar 

  7. R. J. Baxter, J. Stat. Phys. 52:639–667 (1988).

    Google Scholar 

  8. R. J. Baxter, Phys. Lett. A 146:110–114 (1990).

    Google Scholar 

  9. R. J. Baxter, in Proc. Fourth Asia-Pacific Physics Conference, Vol. 1, S. H. Ahn, II-T. Cheon, S. H. Choh, and C. Lee, eds. (World Scientific, Singapore, 1991), pp. 42–57.

    Google Scholar 

  10. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, London and New York, 1982).

    Google Scholar 

  11. R. J. Baxter, J. Stat. Phys. 70:535–582 (1993).

    Google Scholar 

  12. G. Albertini, B. M. McCoy, J. H. H. Perk, and S. Tang, Nucl. Phys. B 314:741–763 (1989).

    Google Scholar 

  13. M. Henkel and J. Lacki, Phys. Lett. A 138:105–109 (1989).

    Google Scholar 

  14. M. Jimbo, T. Miwa, and A. Nakayashiki, J. Phys. A 26:2199–2210 (1993).

    Google Scholar 

  15. M. Jimbo, R. Kedem, H. Konno, T. Miwa, and R. Weston, Nucl. Phys. B 448:429–456 (1995).

    Google Scholar 

  16. O. Foda, M. Jimbo, K. Miki, T. Miwa, and A. Nakayashiki, J. Math. Phys. 35:13–46 (1994).

    Google Scholar 

  17. B. Davies, in Confronting the Infinite, A. L. Carey et al, eds. (World Scientific, Singapore, 1995), pp. 175–192.

    Google Scholar 

  18. M. Yu. Lashkevich, Mod. Phys. Lett. B 10:101–116 (1996).

    Google Scholar 

  19. B. Davies and I. Peschel, Ann. Physik 6:187–214 (1997).

    Google Scholar 

  20. R. J. Baxter, in Proceedings of the International Conference on Frontiers in Quantum Physics, Kuala Lumpur, 1997, S. C. Lim, ed. (1998).

  21. V. Lakshmikantham and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications (Academic, San Diego, 1988).

    Google Scholar 

  22. R. J. Baxter, J. Stat. Phys. 28:1–41 (1982).

    Google Scholar 

  23. R. J. Baxter, Physica 18D:321–347 (1986).

    Google Scholar 

  24. R. J. Baxter, in Proceedings of the International Congress of Mathematicians, Kyoto, 1990 (Springer-Verlag, Tokyo, 1991), pp. 1305–1317.

    Google Scholar 

  25. R. J. Baxter, in Integrable Quantum Field Theories, L. Bonora et al., eds. (Plenum Press, New York, 1993), pp. 27–37.

    Google Scholar 

  26. O. Ore, The Four-Color Problem (Aademic Press, New York, 1967).

    Google Scholar 

  27. M. Kashiwara and T. Miwa, Nucl. Phys. B275[FS17]:121–134 (1986).

    Google Scholar 

  28. V. B. Matveev and A. O. Smirnov, Letters in Math. Phys. 19:179–185 (1990).

    Google Scholar 

  29. R. J. Baxter, Phil. Trans. Roy. Soc. 289:315–346 (1978).

    Google Scholar 

  30. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1965).

    Google Scholar 

  31. L. Onsager, Nuovo Cimento (Suppl.) 6:261 (1949).

    Google Scholar 

  32. C. N. Yang, Phys. Rev. 85:808–816 (1952).

    Google Scholar 

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Baxter, R.J. Functional Relations for the Order Parameters of the Chiral Potts Model. Journal of Statistical Physics 91, 499–524 (1998). https://doi.org/10.1023/A:1023096408679

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