Abstract
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
L. Dolan and M. Grady, Phys. Rev. D 25:1587–1604 (1982).
S. Howes, L. P. Kadanoff, and M. den Nijs, Nucl. Phys. B 215[FS7]:169–208 (1983).
G. von Gehlen and V. Rittenberg, Nucl. Phys. B 257[FS14]:351–370 (1985).
H. Au-Yang, B. M. McCoy, J. H. H. Perk, S. Tang, and M.-L. Yan, Phys. Lett. A 123:219–223 (1987).
B. M. McCoy, J. H. H. Perk, and S. Tang, Phys. Lett. A 125:9–14 (1987).
R. J. Baxter, J. H. H. Perk, and H. Au-Yang, Phys. Lett. A 128:138–142 (1988).
R. J. Baxter, J. Stat. Phys. 52:639–667 (1988).
R. J. Baxter, Phys. Lett. A 146:110–114 (1990).
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.
R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, London and New York, 1982).
R. J. Baxter, J. Stat. Phys. 70:535–582 (1993).
G. Albertini, B. M. McCoy, J. H. H. Perk, and S. Tang, Nucl. Phys. B 314:741–763 (1989).
M. Henkel and J. Lacki, Phys. Lett. A 138:105–109 (1989).
M. Jimbo, T. Miwa, and A. Nakayashiki, J. Phys. A 26:2199–2210 (1993).
M. Jimbo, R. Kedem, H. Konno, T. Miwa, and R. Weston, Nucl. Phys. B 448:429–456 (1995).
O. Foda, M. Jimbo, K. Miki, T. Miwa, and A. Nakayashiki, J. Math. Phys. 35:13–46 (1994).
B. Davies, in Confronting the Infinite, A. L. Carey et al, eds. (World Scientific, Singapore, 1995), pp. 175–192.
M. Yu. Lashkevich, Mod. Phys. Lett. B 10:101–116 (1996).
B. Davies and I. Peschel, Ann. Physik 6:187–214 (1997).
R. J. Baxter, in Proceedings of the International Conference on Frontiers in Quantum Physics, Kuala Lumpur, 1997, S. C. Lim, ed. (1998).
V. Lakshmikantham and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications (Academic, San Diego, 1988).
R. J. Baxter, J. Stat. Phys. 28:1–41 (1982).
R. J. Baxter, Physica 18D:321–347 (1986).
R. J. Baxter, in Proceedings of the International Congress of Mathematicians, Kyoto, 1990 (Springer-Verlag, Tokyo, 1991), pp. 1305–1317.
R. J. Baxter, in Integrable Quantum Field Theories, L. Bonora et al., eds. (Plenum Press, New York, 1993), pp. 27–37.
O. Ore, The Four-Color Problem (Aademic Press, New York, 1967).
M. Kashiwara and T. Miwa, Nucl. Phys. B275[FS17]:121–134 (1986).
V. B. Matveev and A. O. Smirnov, Letters in Math. Phys. 19:179–185 (1990).
R. J. Baxter, Phil. Trans. Roy. Soc. 289:315–346 (1978).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1965).
L. Onsager, Nuovo Cimento (Suppl.) 6:261 (1949).
C. N. Yang, Phys. Rev. 85:808–816 (1952).
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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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DOI: https://doi.org/10.1023/A:1023096408679