Functional equations and fusion matrices for the eight vertex model

Publications of the Research Institute for Mathematical Sciences

Volumn 40, Issue 3, 2004, Pages 905-932

  Fabricius, Klaus ^a   McCoy, Barry M ^b  

^a UNIVERSITY OF WUPPERTAL   (Germany)

^b STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9544223175     PISSN: 00345318     EISSN: 16634926     Source Type: Journal    
DOI: 10.2977/prims/1145475496     Document Type: Article

References (25)

1. Baxter, R. J., Partition function of the eight vertex lattice model, Ann. Phys., 70 (1972), 193-228.
2. Au-Yang, H., McCoy, B. M., Perk, J. H. H., Tang, S. and Van, M-L., Commuting transfer matrices in the chiral Potts model: solutions of the star triangle equations with genus >1, Phys. Lett. A, 123 (1987), 219-223.
3. Bazhanov, V. V. and Stroganov, Yu. G., Chiral Potts model as a descendant of the six-vertex model, J. Stat. Phys., 59 (1990), 799-817.
4. Albertini, G., McCoy, B. M. and Perk, J. H. H., Commensurate-incommensurate transition in the ground state of the superintegrable chiral Potts model, Phys. Lett. A, 135 (1989), 159-166.
5. _, Eigenvalue spectrum of the superintegrable chiral Potts model, Adv. Stud. Pure Math., 19, ed. Jimbo, M., Miwa, T. and Tsuchiya, A., Kinikuniya-Academic Press, Tokyo, (1989), 1-55.
6. Baxter, R. J., Bazhanov, V. V. and Perk, J. H. H., Functional relations for transfer matrices of the chiral Potts model, Int. J. Mod. Phys. B, 4 (1990), 803-870.
7. Baxter, R. J., Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain I: Some fundamental eigenvectors, Ann. Phys., 76 (1973), 1-24.
8. _, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain II: Equivalence to a generalized Ice-type lattice model, Ann. Phys., 76 (1973), 25-47.
9. _, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain III: Eigenvectors of the transfer matrix and the Hamiltonian, Ann. Phys., 76 (1973), 48-71.
10. Fabricius, K. and McCoy, B. M., New developments in the eight vertex model, J. Stat. Phys., 111 (2003), 323-337.
11. Kulish, P. P. and Reshetikhin, N. Yu., Quantum linear problem for the sine-Gordon and higher representations, J. Soviet Math., 23 (1983), 2435; translated from Zap. Nauch. Sem., LOMI, 101 (1981), 101-110.
12. Kulish, P. P. and Reshetikhin, N. Yu., Quantum linear problem for the sine-Gordon and higher representations, J. Soviet Math., 23 (1983), 2435; translated from Zap. Nauch. Sem., LOMI, 101 (1981), 101-110.
13. Kulish, P. P., Reshetikhin, N. Yu. and Sklyanin, E. K., Yang Baxter equation and representation theory, Lett. Math. Phys., 5 (1981), 393-403.
14. Sklyanin, E. K., Some algebraic structures connected with the Yang-Baxter equation, Funct. Anal. Appl., 16 (1982), 27-34.
15. _, Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras, Funct. Anal. Appl., 17 (1984), 34-48.
16. Date, E., Jimbo, M., Miwa, T. and Okado, M., Fusion of the eightvertex SOS model, Lett. Math. Phys., 12 (1986), 209-215.
17. Kirillov, A. N. and Reshetikhin N. Yu., Exact solution of the integrable XXZ Heisenberg model with arbitrary spin I. The ground state and the excitation spectrum, J. Phys. A, 20 (1987), 1565-1585.
18. Date, E., Jimbo, M., Kuniba, A., Miwa, T. and Okado, M., Exactly solvable SOS models, II. Proof of the star triangle relation and combinatorial identities, Adv. Stud. Pure Math., 16 (1988), 17-122.
19. Nepomechie, R. I., Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity, Nucl. Phys. B, 622 (2002), 615-632.
20. _, Functional relations and Bethe ansatz for the XXZ chain, J. Stat. Phys., 111 (2003), 1363-1376.
21. _, Bethe ansatz solution of the open XXZ chain with nondiagonal boundary terms, hepth/0304092.
22. Bazhanov, V. V. and Reshetikhin, N. Yu., Critical RSOS models and conformal field theory, Int. J. Mod. Phys. A, 4 (1989), 115-142.
23. Baxter, R. J., private communication.
24. Weber, H., Lehrbuch der Algebra, B.III. Elliptische Funktionen und Algebraische Zahlen, F. Vieweg und Sohn, Braunschweig, 1908.
25. Baxter, R. J., Exactly solved models, Academic Press, London, 1982.