Literature cited
H. Au-Yang, B. McCoy, J. H. H. Perk, S. Tang, and M. L. Yan, “Commuting transfer matrices in the chiral Potts models: solutions of star-triangle equations with genus 1,” Phys. Lett. A,123, No. 5, 219–223 (1987).
B. McCoy, J. H. H. Perk, S. Tang, and C. H. Sah, “Commuting transfer matrices for the four-state self-dual chiral Potts model with a genus-three uniformizing Fermat curve,” Phys. Lett. A,125, No. 1, 9–14 (1987).
R. J. Baxter J. H. H. Perk, and H. Au-Yang, “New solutions of star-triangle relations for the chiral Potts model,” Phys. Lett. A,128, No. 3, 138–142 (1988).
R. J. Baxter, “Free energy of the solvable chiral Potts model,” J. Stat. Phys.,52, 639–667 (1988).
R. J. Baxter, “The superintegrable chiral Potts model,” Phys. Lett. A (in press).
J. H. H. Perk, “Onsager star-triangle equation: master key to integrability,” Proc. of Tuniguchi Conf. Kyoto (October, 1988).
R. J. Baxter, “Solving models in statistical mechanics,” Preprint, University of Canberra (1988), to appear in Proc. of Tuniguchi Conf. Kyoto (October, 1988).
G. Albertiny, B. McCoy, and J. H. H. Perk, “First-order transition in the ground state of the superintegrable chiral Potts model,” Preprint, SUNY Stony Brook. ITP-SB-88-58 (1988).
V. V. Bazhanov and N. Yu. Reshetikhin, “Critical RSOS models and conformal field theory,” Preprint Institute for High Energy Physics. IFVE 87-102, 1–31 (1987).
V. B. Matveev and A. O. Smirnov, “On the Riemann theta function of a trigonal curve and solutions of the Boussinesq and KP equations,” Lett. Math. Phys.,14, 25–31 (1987).
E. D. Belokolos, A. I. Bobenko, V. B. Matveev, and V. Z. Énol'skii, “Algebraic-geometric principals of the superposition of finite-zoned solutions of integrable nonlinear equations,” Usp. Mat. Nauk,41, No. 2, 3–42 (1986).
A. O. Smirnov, “The matrix analogue of a theorem of Appell and reductions of multidimensional Riemann theta functions,” Mat. Sb.,133, No. 3, 382–391 (1987).
A. O. Smirnov, “Finite-zoned solutions of an abelian Toda chain of genus 4 and 5 in elliptic functions,” Teor. Mat. Fiz.,78, No. 1, 11–21 (1989).
M. V. Babich, A. I. Bobenko, and V. B. Matveev, “Reductions of Riemann theta functions of genus g to theta functions of lower genera and symmetric algebraic curves,” Dokl. Akad. Nauk SSSR,272, No. 1, 13–17 (1983).
R. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, London -New York (1982).
G. Albertini, B. McCoy, and J. H. H. Perk, “Eigenvalue spectrum of the superintegrable chiral Potts model,” Preprint ITP-SB-89-1, 1–63 (1989).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 46, No. 3, pp. 31–39, September, 1989.
Rights and permissions
About this article
Cite this article
Matveev, V.B., Smirnov, A.O. Star-triangle equations and some properties of algebraic curves connected with the integrable chiral Potts model. Mathematical Notes of the Academy of Sciences of the USSR 46, 701–706 (1989). https://doi.org/10.1007/BF01158372
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01158372