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.
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References
L. Onsager,Phys. Rev. 65:117 (1944).
R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
L. D. Faddeev,Sov. Sci. Rev. C 1:107–155 (1980).
H. Au-Yang, B. M. McCoy, J. H. H. Perk, S. Tang, and M. Yan,Phys. Lett. A 123:219 (1987).
B. M. McCoy, J. H. H. Perk, S. Tang, and C. H. Sah,Phys. Lett. A 125:9 (1987).
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).
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).
L. Dolan and M. Grady,Phys. Rev. D 25:1587 (1982).
S. Howes, L. P. Kadanoff, and M. den Nijs,Nucl. Phys. B 215[FS7]:169 (1983).
G. von Gehlen and V. Rittenberg,Nucl. Phys. B 257[FS14]:351 (1985).
E. H. Lieb,Phys. Rev. 162:162 (1967);Phys. Lett. 18:1046,19:108 (1967).
B. Sutherland,Phys. Rev. Lett. 19:103 (1967).
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).
G. Albertini, B. M. McCoy, and J. H. H. Perk,Phys. Lett. A 139:204 (1989).
G. Albertini, B. M. McCoy, and J. H. H. Perk,Phys. Lett. A 135:159 (1989).
R. J. Baxter,Phys. Lett. A 133:185 (1988).
R. J. Baxter, A simple solvableZ n Hamiltonian,Phys. Lett. A, to appear.
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.
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.
V. G. Drinfeld, “Quantum Groups,”Proc. Int. Congress of Mathematics, Berkeley, 1987, pp. 798–820.
L. D. Faddeev, N. Yu. Reshetikhin, and L. A. Takhtajan,Algebra Analiz 1(1):178 (1989).
E. K. Sklyanin,Funk. Anal. Prilozh. 16(4):27 (1982).
V. A. Fateev and A. B. Zamolodchikov,Phys. Lett. A 92:37 (1982).
A. G. Izergin and V. E. Korepin,Nucl. Phys. B 205:401 (1982); V. O. Tarasov,Teor. Mat. Fiz. 63(2):175 (1985).
R. J. Baxter,Ann. Phys. 76:1 (1973).
V. B. Matveev and A. O. Smirnov, Some comments on the solvable chiral Potts model,Lett. Math. Phys. (1989).
A. N. Kirillov and N. Y. Reshetikhin,J. Phys. A: Math. Gen. 19:565 (1986).
Y. E. Korepin and V. O. Tarasov. Private communication.
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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
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DOI: https://doi.org/10.1007/BF01025851