Some remarks on a generalization of the superintegrable chiral Potts model

Journal of Statistical Physics

Volumn 137, Issue 5, 2009, Pages 798-813

  Baxter, R J ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Lattice models; Statistical mechanics; Transfer matrices

Indexed keywords

EID: 74449091543     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9778-1     Document Type: Article

References (22)

1. Onsager, L.: Crystal statistics. I. A two-dimensional Ising model with an order-disorder transition. Phys. Rev. 65, 117-149 (1944).
2. Kaufman, B.: Crystal statistics. II. Partition function evaluated by spinor analysis. Phys. Rev. 76, 1232-1243 (1949).
3. Kac, M., Ward, J. C.: A combinatorial solution of the two-dimensional Ising model. Phys. Rev. 88, 1332-1337 (1952).
4. Hurst, C. A., Green, H. S.: New solution of the Ising problem for a rectangular lattice. J. Chem. Phys. 33, 1059-1062 (1960).
5. Kasteleyn, P. W.: The statistics of dimers on a lattice. Physica 27, 1209-1225 (1961).
6. Temperley, H. N. V., Fisher, M. E.: Dimer problem in statistical mechanics: an exact result. Philos. Mag. 6, 1061-1063 (1961).
7. Fisher, M. E.: Statistical mechanics of dimers on a plane lattice. Phys. Rev. 124, 1664-1672 (1961).
8. Kasteleyn, P. W.: Dimer statistics and phase transitions. J. Math. Phys. 4, 287-293 (1963).
9. Onsager, L.: In: Proceedings of the IUPAP Conference on Statistical Mechanics, Discussione e Observazioni. Nuovo Cimento (Suppl), Series 9, vol. 6, p. 261 (1949).
10. Yang, C. N.: The spontaneous magnetization of a two-dimensional Ising model. Phys. Rev. 85, 808-816 (1952).
11. Montroll, E. W., Potts, R. B., Ward, J. C.: Correlations and spontaneous magnetization of the two-dimensional Ising model. J. Math. Phys. 4, 308-322 (1963).
12. Baxter, R. J., Perk, J. H. H., Au-Yang, H.: New solutions of the star-triangle relations for the chiral Potts model. Phys. Lett. A 128, 138-142 (1988).
13. Baxter, R. J.: Free energy of the solvable chiral Potts model. J. Stat. Phys. 52, 639-667 (1988).
14. Baxter, R. J.: The order parameter of the chiral Potts model. J. Stat. Phys. 120, 1-36 (2005).
15. Albertini, G., McCoy, B. M., Perk, J. H. H., Tang, S.: Excitation spectrum and order parameter for the integrable N-state chiral Potts model. Nucl. Phys. B 314, 741-763 (1989).
16. Baxter, R. J.: A conjecture for the superintegrable chiral Potts model. J. Stat. Phys. 132, 983-1000 (2008).
17. Au-Yang, H., McCoy, B. M., Perk, J. H. H., Tang, S.: Solvable models in statistical mechanics and Riemann surfaces of genus greater than one. In: Algebraic Analysis, vol. 1, pp. 29-37. Academic Press, Tokyo (1988).
18. Au-Yang, H., Perk, J. H. H.: Onsager's star-triangle relation: master key to integrability. Adv. Stud. Pure Math. 19, 57-94 (1989).
19. Davies, B.: Onsager's algebra and integrability. J. Phys. A, Math. Gen. 23, 2245-2261 (1990).
20. Baxter, R. J.: The superintegrable chiral Potts model. Phys. Lett. A 133, 185-189 (1988).
21. Baxter, R. J.: Superintegrable chiral Potts model: thermodynamic properties, an "inverse" model, and a simple associated Hamiltonian. J. Stat. Phys. 57, 1-39 (1989).
22. Nishino, A., Deguchi, T.: The L(sl2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model. Phys. Lett. A 356, 366-370 (2006).