The many faces of the chiral Potts model

International Journal of Modern Physics B

Volumn 11, Issue 1-2, 1997, Pages 11-26

  Au Yang, Helen ^a   Perk, Jacques H H ^a  

^a OKLAHOMA STATE UNIVERSITY   (United States)

Author keywords

(affine) quantum groups; Basic hypergeometric functions; Chiral Potts model; Cyclic representations; Star triangle equation; Yang Baxter equation

Indexed keywords

EID: 0003090766     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0217979297000046     Document Type: Article

References (66)

1. F. Y. Wu and Y. K. Wang, J. Math. Phys. 17, 439 (1976).
2. S. Ostlund, Phys. Rev. B24, 398 (1981).
3. D. A. Huse, Phys. Rev. B24, 5180 (1981).
4. D. A. Huse, A. M. Szpilka, and M. E. Fisher, Physica, A121, 363 (1983).
5. M. P. M. den Nijs, in Phase Transitions and Critical Phenomena, eds. C. Domb and J. L. Lebowitz (Academic, London, 1988), Vol. 12, p. 219.
6. W. Selke, Phys. Repts. 170, 213 (1988).
7. H. Au-Yang and J. H. H. Perk, J. Stat. Phys. 78, 17 (1995).
8. M. N. Barber, J. Phys. A15, 915 (1982).
9. D. A. Huse and M. E. Fisher, J. Phys. C15, L585 (1982).
10. H. Au-Yang and J. H. H. Perk, in STATPHYS 19, ed. Hao Bailin (World Scientific, Singapore, 1996), p. 421.
11. H. Au-Yang and J. H. H. Perk, Physica A177, 139 (1991).
12. H. Au-Yang, B. M. McCoy, J. H. H. Perk, S. Tang, and M. L. Yan, Phys. Lett. A123, 219 (1987).
13. H. Au-Yang, B. M. McCoy, J. H. H. Perk, and S. Tang, in Algebraic Analysis, Vol. 1, eds. M. Kashiwara and T. Kawai (Academic, San Diego, 1988), p. 29.
14. R. J. Baxter, J. H. H. Perk, and H. Au-Yang, Phys. Lett. A128, 138 (1988).
15. H. Au-Yang and J. H. H. Perk, Adv. Stud. Pure Math. 19, 57 (1989).
16. G. Albertini, B. M. McCoy, and J. H. H. Perk, Adv. Stud. Pure Math. 19, 1 (1989); Phys. Lett. A135, 159 (1989), A139, 204 (1989).
17. G. Albertini, B. M. McCoy, and J. H. H. Perk, Adv. Stud. Pure Math. 19, 1 (1989); Phys. Lett. A135, 159 (1989), A139, 204 (1989).
18. G. Albertini, B. M. McCoy, and J. H. H. Perk, Adv. Stud. Pure Math. 19, 1 (1989); Phys. Lett. A135, 159 (1989), A139, 204 (1989).
19. V. A. Fateev and A. B. Zamolodchikov, Phys. Lett. A92, 37 (1982).
20. G. Albertini, B. M. McCoy, J. H. H. Perk, and S. Tang, Nucl. Phys. B314, 741 (1989).
21. B. M. McCoy and S.-S. Roan, Phys. Lett. A150, 347 (1990).
22. R. J. Baxter, J. Stat. Phys. 52, 639 (1988).
23. R. J. Baxter, J. Stat. Phys. 57, 1 (1989).
24. R. J. Baxter, in Calculation of the Eigenvalues of the Transfer Matrix of the Chiral Potts Model, Proc. of Fourth Asia Pacific Physics Conference (World Scientific, Singapore, 1991), p. 42.
25. R. J. Baxter, J. Stat. Phys. 82, 1219 (1996).
26. R. J. Baxter, V. V. Bazhanov, and J. H. H. Perk, Intern. J. Mod. Phys. B4, 803 (1990).
27. R. J. Baxter, J. Stat. Phys. 73, 461 (1993), J. Phys. A27, 1837 (1994).
28. R. J. Baxter, J. Stat. Phys. 73, 461 (1993), J. Phys. A27, 1837 (1994).
29. R. J. Baxter, M. J. O'Rourke and R. J. Baxter, J. Stat. Phys. 82, 1 (1996).
30. H. Au-Yang and J. H. H. Perk, Intern. J. Mod. Phys. A7, Suppl. 1B, 1007, 1025 (1992).
31. W. S. McCullough, J. H. H. Perk, and H. L. Scott, J. Chem. Phys. 93, 6070 (1990).
32. H. Au-Yang and J. H. H. Perk, Intern. J. Mod. Phys. (Proc. Suppl.) 3A, 430 (1993).
33. C. De Concini and V. G. Kac, in Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, eds. A. Connes, M. Duflo, A. Joseph, and R. Rentschier (Birkhäuser, Boston, 1990), p. 471.
34. S. Howes, L. P. Kadanoff, and M. den Nijs, Nucl. Phys. B215[FS7], 169 (1983).
35. G. von Gehlen and V. Rittenberg, Nucl. Phys. B257[FS14|, 351 (1985).
36. J. H. H. Perk, Proc. Symp. Pure Math. 49, part 1, 341 (1989).
37. B. Davies, J. Math. Phys. 32, 2945 (1991).
38. V. V. Bazhanov and R. J. Baxter, J. Stat. Phys. 69, 453 (1992), 71, 839 (1993).
39. V. V. Bazhanov and R. J. Baxter, J. Stat. Phys. 69, 453 (1992), 71, 839 (1993).
40. R. M. Kashaev, V. V. Mangazeev, and Yu. G. Stroganov, Intern. J. Mod. Phys. A8, 587,1399 (1993).
41. V. V. Mangazeev, S. M. Sergeev, and Yu. G. Stroganov, Intern. J. Mod. Phys. A9, 5517 (1994); Mod. Phys. Lett. A10, 279 (1995).
42. V. V. Mangazeev, S. M. Sergeev, and Yu. G. Stroganov, Intern. J. Mod. Phys. A9, 5517 (1994); Mod. Phys. Lett. A10, 279 (1995).
43. G. E. Boos, V. V. Mangazeev, and S. M. Sergeev, Intern. J. Mod. Phys. A10, 4041 (1996).
44. S. M. Sergeev, G. E. Boos, V. V. Mangazeev, and Yu. G. Stroganov, Mod. Phys. Lett. A11, 491 (1996).
45. G. E. Boos, Intern. J. Mod. Phys. A11, 313 (1996).
46. Z. N. Hu, Intern. J. Mod. Phys. A9, 5201 (1994); Phys. Lett. A197, 387 (1995).
47. Z. N. Hu, Intern. J. Mod. Phys. A9, 5201 (1994); Phys. Lett. A197, 387 (1995).
48. Z. N. Hu and B. Y. Hou, J. Stat. Phys. 79, 759 (1995), 82, 633 (1996).
49. Z. N. Hu and B. Y. Hou, J. Stat. Phys. 79, 759 (1995), 82, 633 (1996).
50. S. M. Sergeev, V. V. Mangazeev, and Yu. G. Stroganov, J. Stat. Phys. 82, 31 (1996).
51. E. Date, M. Jimbo, K. Miki and T. Miwa, Comm. Math. Phys. 137, 133 (1991); Publ. RIMS, Kyoto Univ. 27, 347, 639 (1991).
52. E. Date, M. Jimbo, K. Miki and T. Miwa, Comm. Math. Phys. 137, 133 (1991); Publ. RIMS, Kyoto Univ. 27, 347, 639 (1991).
53. V. V. Bazhanov, R. M. Kashaev, V. V. Mangazeev, and Yu. G. Stroganov, Comm. Math. Phys. 138, 393 (1991).
54. R. M. Kashaev, V. V. Mangazeev and T. Nakanishi, Nucl. Phys. B362, 563 (1991).
55. R. M. Kashaev and V. V. Mangazeev, Mod. Phys. Lett. A7, 2827 (1992).
56. H. Au-Yang and J. H. H. Perk, Physica A228, 78 (1996).
57. V. V. Bazhanov and Yu. G. Stroganov, J. Stat. Phys. 59, 799 (1990).
58. I. G. Korepanov, unpublished reports (in Russian, for more details see also preprint hep-th/941006).
59. V. O. Tarasov, Int. J. Mod. Phys. A7, Suppl. 1B, 963 (1992); Comm. Math. Phys. 158, 459 (1993).
60. V. O. Tarasov, Int. J. Mod. Phys. A7, Suppl. 1B, 963 (1992); Comm. Math. Phys. 158, 459 (1993).
61. C. Gómez, M. Ruiz-Altaba and G. Sierra, Phys. Lett. B265, 95 (1991).
62. I. T. Ivanov and D. B. Uglov, Phys. Lett. A167, 459 (1992).
63. A. Schnizer, J. Math. Phys. 34, 4340 (1993); Comm. Math. Phys. 163, 293 (1994).
64. A. Schnizer, J. Math. Phys. 34, 4340 (1993); Comm. Math. Phys. 163, 293 (1994).
65. W. N. Bailey, Generalized Hypergeometric Series (Cambridge Univ. Press, Cambridge, 1935), pp. 65-70.
66. L. J. Slater, Generalized Hypergeometric Functions (Cambridge Univ. Press, Cambridge, 1966), Ch. 3, App. II, IV.