Fermionic solution of the Andrews-Baxter-Forrester model. I. Unification of TBA and CTM methods

Journal of Statistical Physics

Volumn 82, Issue 3-4, 1996, Pages 657-685

  Warnaar, S Ole ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

ABF model; Corner transfer matrices; One dimensional fermi gas; Rogers ramanujan identities; Thermodynamic bethe ansatz

Indexed keywords

EID: 0001011048     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02179790     Document Type: Article

References (52)

1. C. N. Yang and C. P. Yang, J. Math. Phys. 10:1115 (1969).
2. M. Takahashi, Prog. Theor. Phys. 46:401 (1971).
3. M. Takahashi and M. Suzuki, Prog. Theor. Phys. 48:2187 (1972).
4. V. V. Bazhanov and N. Yu Reshetikhin, Int. J. Mod. Phys. A 4:115 (1989).
5. V. V. Bazhanov and N. Yu Reshetikhin, J. Phys. A: Math. Gen. 23:1477 (1990).
6. V. V. Bazhanov and N. Yu Reshetikhin, Prog. Theor. Phys. 102:301 (1990).
7. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
8. G. Albertini, S. Dasmahapatra, and B. M. McCoy, Int. J. Mod. Phys. A 7 (Suppl. 1A): 1 (1992).
9. G. E. Andrews, R. J. Baxter, and P. J. Forrester, J. Stat. Phys. 35:193 (1984).
10. E. Melzer, Int. J. Mod. Phys. A 9:1115 (1994).
11. R. Kedem, T. R. Klassen, B. M. McCoy, and E. Melzer, Phys. Lett. 304B:263 (1993).
12. A. Berkovich, Nucl. Phys. B 431:315 (1994).
13. R. Kedem and B. M. McCoy, J. Stat. Phys. 71:883 (1993).
14. S. Dasmahapatra, R. Kedem, B. M. McCoy, and E. Melzer, J. Stat. Phys. 74:239 (1994).
15. S. Dasmahapatra, R. Kedem, T. R. Klassen, B. M. McCoy, and E. Melzer, Int. J. Mod. Phys. B 7:3617 (1993).
16. R. Kedem, T. R. Klassen, B. M. McCoy, and E. Melzer, Phys. Lett. 307B:68 (1993).
17. M. Jimbo, T. Miwa, and M. Okado, Nucl. Phys. B 300[FS22]:74 (1988).
18. A. Kuniba, T. Nakanishi, and J. Suzuki, Mod. Phys. Lett. A 8:1649 (1993).
19. S. Dasmahapatra, String hypothesis and characters of coset CFT's, Preprint ICTP IC/93/91 [hep-th/9305024].
20. E. Melzer, Lett. Math. Phys. 31:233 (1994).
21. S. Dasmahapatra, On state counting and characters, Preprint CMPS 94-103 [hep-th/ 9404116].
22. O. Foda and Y.-H. Quano, Int. J. Mod. Phys. A 10:2291 (1995).
23. S. O. Warnaar and P. A. Pearce, J. Phys. A: Math. Gen. 27:L891 (1994).
24. S. O. Warnaar and P. A. Pearce, A-D-E polynomial and Rogers-Ramanujan identities, Preprint University of Melbourne No. 41-94 [hep-th/9411009]. To appear in Int. J. Mod. Phys. A.
25. A. Berkovich and B. M. McCoy, Continued fractions and fermionic representations for characters of M(p, p′) minimal models, Preprint BONN-TH-94-28, ITPSB 94-060 [hep-th/9412030]. To appear in Lett. Math. Phys.
26. E. Melzer, Supersymmetric analogs of the Gordon-Andrews identities, and related TBA systems, Preprint TAUP 2211-94 [hep-th/9412154].
27. D. A. Huse, Phys. Rev. Lett. 49:1121 (1982).
28. R. J. Baxter, J. Stat. Phys. 26:427 (1981).
29. G. E. Andrews, The Theory of Partitions (Addison-Wesley, Reading, Massachusetts, 1976).
30. A. Rocha-Caridi, in Vertex Operators in Mathematics and Physics, J. Lepowsky, S. Mandelstam, and I. M. Singer, eds. (Springer, Berlin, 1985).
31. D. Bressoud, Lecture Notes in Mathematics, Vol. 1395 (Springer, Berlin, 1987), p. 140.
32. J. Kellendonk, M. Rösgen, and R. Varnhagen, Int. J. Mod. Phys. A 9:1009 (1994).
33. M. Rösgen and R. Varnhagen, Steps towards lattice Virasoro algebras: su(I, I), Preprint BONN-TH-94-23 [hep-th/9501005].
34. A. Berkovich, Private communication.
35. A. B. Zamolodchikov and V. A. Fateev, Sov. Phys. JETP 62:215 (1985).
36. I:(AMS, Providence. Rhode Island, 1985).
37. A. Berkovich, C. Gomez, and G. Sierra, Nucl. Phys. B 415:681 (1994).
38. B. Richmond and G. Szekeres, J. Aust. Math. Soc. A 31:362 (1981).
39. W. Nahm, A. Recknagel, and M. Terhoeven, Mod. Phys. Lett. A 8:1835 (1993).
40. L. Lewin, Polylogarithms and Associated Functions (Elsevier, Amsterdam, 1981).
41. A. N. Kirillov and N. Yu. Reshetikhin, J. Sov. Math. 52:3156 (1990).
42. I. Affleck, Phys. Rev. Lett. 56:746 (1986).
43. V. V. Bazhanov, S. L. Lukyanov, and A. B. Zamolodchikov, Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz, Preprint CLNS 94/1316 [hep-th/9412229].
44. S. O. Warnaar, Fermionic solution of the Andrews-Baxter-Forrester model II: Proof of Melzer's polynomial identities, Preprint University of Melbourne No. 17-95 [hep-th/ 9508079].
45. A. Kuniba, Nucl. Phys. B 389:209 (1993).
46. V. V. Bazhanov, B. Nienhuis, and S. O. Warnaar, Phys. Lett. 322B:198 (1994).
47. G. E. Andrews, R. J. Baxter, D. M. Bressoud, W. J. Burge, P. J. Forrester, and G. Viennot, Eur. J. Comb. 8:341 (1987).
48. l, l case, Preprint University of Melbourne No. 03-95 [hep-th/9501088]. To appear in Lett. Math. Phys.
49. P. Bouwknegt, A. W. W. Ludwig, and K. Schoutens, Phys. Lett. 338B:448 (1994).
50. P. Bouwknegt, A. W. W. Ludwig, and K. Schoutens, Spinon basis for higher level SU(2) WZW models, Preprint USC-94/20 [hep-th/9412108].
51. 1 conformal field theory, Preprint USC-94/21 [hep-th/9412199].
52. G. Georgiev, Combinatorial construction of modules for infinite-dimensional Lie algebras, I. Principal subspace, Preprint Rutgers University [hep-th/9412054].