Eigenvectors in the superintegrable model I: Sl2 generators

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 27, 2008, Pages

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

^a OKLAHOMA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 48249089269     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/27/275201     Document Type: Article

References (31)

1. Au-Yang H, McCoy B M, Perk J H H, Tang S and Yan M-L 1987 Commuting transfer matrices in the chiral Potts models: solutions of the star-triangle equations with genus >1 Phys. Lett. A 123 219-23
2. McCoy B M, Perk J H H, Tang S and Sah C H 1987 Commuting transfer matrices for the 4 state self-dual chiral Potts model with a genus 3 uniformizing Fermat curve Phys. Lett. A 125 9-14
3. Au-Yang H, McCoy B M, Perk J H H and Tang S 1988 Solvable models in statistical mechanics and Riemann surfaces of genus greater than one Algebraic Analysis vol 1 ed M Kashiwara and T Kawai (San Diego, CA: Academic) pp 29-40
4. Baxter R J, Perk J H H and Au-Yang H 1988 New solutions of the star-triangle relations for the chiral Potts model Phys. Lett. A 128 138-42
5. Au-Yang H and Perk J H H 1989 Onsager's star-triangle equation: master key to integrability Advanced Studies in Pure Mathematics vol 19 (Tokyo: Kinokuniya Academic) pp 57-94
6. Baxter R J 1991 Calculation of the eigenvalues of the transfer matrix of the chiral Potts model Proc. 4th Asia Pacific Physics Conference (Singapore: World Scientific) pp 42-58
7. Baxter R J 2005 Derivation of the order parameter of the chiral Potts model Phys. Rev. Lett. 94 130606
8. Baxter R J 1998 Functional relation for the order parameters of the chiral Potts model J. Stat. Phys. 91 499-523
9. Baxter R J 2005 The order parameter of the chiral Potts model J. Stat. Phys. 120 1-36
10. Onsager L 1944 Crystal statistics: I. A two-dimensional model with an order-disorder transition Phys. Rev. 65 117-49
11. Yang C N 1952 The spontaneous magnetization of a two-dimensional Ising model Phys. Rev. 85 808-16
12. Korepanov I G 2000 The method of vacuum vectors in the theory of Yang-Baxter equation pp 1-8 (Preprint nlin/0010024) and references cited
13. Baxter R J, Bazhanov V V and Perk J H H 1990 Functional relations for transfer matrices of the chiral Potts model Int. J. Mod. Phys. B 4 803-70
14. Bazhanov V V and Stroganov Yu G 1990 Chiral Potts model as a descendent of the six-vertex model J. Stat. Phys. 59 799-817
15. Baxter R J 1978 Solvable eight-vertex model on an arbitrary planar lattice Phil. Trans. R. Soc. A 289 315-46
16. Iorgov N 2006 Eigenvectors of open Bazhanov-Stroganov quantum chain SIGMA 2 019
17. von Gehlen G, Iorgov N, Pakuliak S and Shadura V 2006 The Baxter-Bazhanov-Stroganov model: Separation of variables and the Baxter equation J. Phys. A: Math. Gen. 39 7257-82
18. von Gehlen G, Iorgov N, Pakuliak S, Shadura V and Tykhyy Yu 2007 Form-factors in the Baxter-Bazhanov-Stroganov model I: norms and matrix elements J. Phys. A: Math. Theor. 40 14117-38
19. Baxter R J 1989 The superintegrable chiral Potts model: thermodynamic properties, an "inverse model", and a simple associated Hamiltonian J. Stat. Phys. 57 1-39
20. Baxter R J 1993 Chiral Potts model with skewed boundary conditions J. Stat. Phys. 73 461-95
21. Baxter R J 1994 Interfacial tension of the chiral Potts model J. Phys. A: Math. Gen. 27 1837-49
22. Tarasov V 1990 Transfer matrix of the superintegrable chiral Potts model. Bethe ansatz spectrum Phys. Lett. A 147 487-90
23. 2 loop algebra at roots of unity J. Phys. A: Math. Theor. 40 7473-508
24. Jimbo M 1992 Topics from representations of -an introductory guide to physicists Quantum Groups and Quantum Integrable Systems Nankai Lectures on Mathematical Physics ed M-L Ge (Singapore: World Scientific) pp 1-61
25. Nishino A and Deguchi T 2006 The symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model Phys. Lett. A 356 366-70
26. 2 loop algebra and the dimensions of reducible representations J. Stat. Mech. p 05007
27. Andrews G E, Askey R and Roy R 1999 Special Functions (Cambridge: Cambridge University Press) chapter 10 pp 484 chapter 10 equation (10.0.8)
28. Deguchi T, Fabricius K and McCoy B M 2001 The symmetry of the six-vertex model at roots of unity J. Stat. Phys. 102 701-36
29. Chari V and Pressley A 1994 A Guide to Quantum Groups (Cambridge: Cambridge University Press) chapter 12 pp 399-403
30. Davies B 1990 Onsager's algebra and superintegrability J. Phys. A: Math. Gen. 23 2245-61
31. (2)- model and the root-of-unity symmetry of six-vertex model with arbitrary spin J. Phys. A: Math. Theor. 40 1481-512