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Hyperelliptic parametrisation of the generalised order parameter of the N = 3 chiral Potts model

Published online by Cambridge University Press:  17 February 2009

R. J. Baxter
R. J. Baxter
Affiliation:
Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia.
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Abstract

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It has been known for some time that the Boltzmann weights of the chiral Potts model can be parametrised in terms of hyperelliptic functions. but as yet no such parametrisation has been applied to the partition and correlation functions. Here we show that for N = 3 the function S(tp) that occurs in the recent calculation of the order parameters can he expressed quite simply in terms of such a parametrisation.

Keywords

statistical mechanicslattice modelsorder parameterschiral Potts model
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 3 , January 2006 , pp. 289 - 307
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Albertini, G., McCoy, B. M., Perk, J. H. H. and Tang, S., “Excitation spectrum and order parameter for the integrable N-state chiral Potts model”, Nuc. Phys. B 314 (1989) 741–763.Google Scholar
[2]Au-Yang, H. and Perk, J. H. H., “Onsager's star-triangle equation: master key to integrability”, Adv. Stud. Pure Math. 19 (1989) 57–94.CrossRefGoogle Scholar
[3]Baxter, R. J., “Solvable eight-vertex model on an arbitrary planar lattice”, Phil. Trans. Roy. Soc. (London) 289 (1978) 315–346.Google Scholar
[4]Baxter, R. J., “Corner transfer matrices”, Physica A (1981) 18–27.Google Scholar
[5]Baxter, R. J., Exactly Solved Models in Statistical Mechanics (Academic, London, 1982).Google Scholar
[6]Baxter, R. J., “Free energy of the solvable chiral Potts model”, J. Stat. Phys. 52 (1988) 639–667.Google Scholar
[7]Baxter, R. J., “Chiral Potts model: eigenvalues of the transfer matrix”, Phys. Lett. A 146 (1990) 110–114.CrossRefGoogle Scholar
[8]Baxer, R. J., “Hyperelliptic function parametrization for the chiral Potts model”, in Proc. Intnl. Conf. Mathematicians, Kyoto 1990, (Springer, Tokyo, 1991) 1305–1317.Google Scholar
[9]Baxter, R. J., “Corner transfer matrices of the chiral Potts model. II. The triangular lattice.”, J. Stat. Phys. 70 (1993) 535–582.Google Scholar
[10]Baxter, R. J., “Elliptic parametrization of the three-state chiral Potts model”, in Integrable Quantum Field Theories (ed. Bonora, L. et al. ), (Plenum Press, New York, 1993) 27–37.Google Scholar
[11]Baxter, R. J., “Functional relations for the order parameters of the chiral Potts model”, J. Stat. Phys. 91 (1998) 499–524.CrossRefGoogle Scholar
[12]Baxter, R. J., “Some hyperelliptic function identities that occur in the chiral Potts model”, J. Phys. A 31 (1998) 6807–6818.Google Scholar
[13]Baxter, R. J., “The ‘inversion relation’ method for obtaining the free energy of the chiral Potts model”. Physica A 322 (2003) 407–431.CrossRefGoogle Scholar
[14]Baxter, R. J.. “Derivation of the order parameter of the chiral Potts model”, Phys. Rev. Lett. 94 (2005) 130602.Google Scholar
[15]Baxter, R. J., “The order parameter of the chiral Potts model”, J. Stat. Phys. 120 (2005) 1–36.CrossRefGoogle Scholar
[16]Baxter, R. J., “The challenge of the chiral Potts model”, J. Physics: Conference Ser. (2006) to appear.Google Scholar
[17]Baxter, R. J., Perk, J. H. H. and Au-Yang, H., “New solutions of the star-triangle relations for the chiral Potts model”, Phys. Lett. A 128 (1988) 138–142.CrossRefGoogle Scholar
[18]Jimbo, M., Miwa, T. and Nakayashiki, A., “Difference equations for the correlation functions of the eight-vertex model”, J. Phys. A 26 (1993) 2199–2210.CrossRefGoogle Scholar
[19]Onsager, L., “Crystal statistics. I. A two-dimensional model with an order-disorder transition”, Phys. Rev. 65 (1944) 117–49.Google Scholar
[20]Yang, C. N., “The spontaneous magnetization of a two-dimensional Ising model”, Phys. Rev. 85 (1952) 808–816.CrossRefGoogle Scholar