The modified tetrahedron equation and its solutions

International Journal of Modern Physics A

Volumn 19, Issue SUPPL. 2, 2004, Pages 179-204

  Von Gehlen, G ^a   Pakuliak, S ^b   Sergeev, S ^b,c  

^a UNIVERSITY OF BONN   (Germany)

^b JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^c MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATION; CONFERENCE PAPER; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MATHEMATICS;

EID: 4944256781     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0217751x04020403     Document Type: Conference Paper

References (42)

1. A. B. Zamolodchikov, Commun. Math. Phys. 79, 489 (1981).
2. V. V. Bazhanov and Yu. G. Stroganov, Teor. Mat. Fiz. 52, 105 (1982).
3. J. M. Maillet and F. W. Nijhoff, Phys. Lett. B224, 389 (1989); Nucl. Phys. (Proc.Suppl.) 18B, 212 (1990).
4. J. M. Maillet and F. W. Nijhoff, Phys. Lett. B224, 389 (1989); Nucl. Phys. (Proc.Suppl.) 18B, 212 (1990).
5. R. J. Baxter, Physica 18D, 321 (1986).
6. V. V. Bazhanov and R. J. Baxter, J. Stat. Phys. 69, 453 (1992); 71, 839 (1993).
7. V. V. Bazhanov and R. J. Baxter, J. Stat. Phys. 69, 453 (1992); 71, 839 (1993).
8. R. J. Baxter, Commun. Math. Phys. 88, 185 (1983).
9. R. J. Baxter and P. J. Forrester, J. Phys. A18, 1483 (1985).
10. V. V. Mangazeev and Yu. G. Stroganov, Mod. Phys. Lett. A8, 3475 (1993).
11. H. E. Boos, V. V. Mangazeev and S. M. Sergeev, Int. J. Mod. Phys. A10, 4041 (1995).
12. I. G. Korepanov, [solv-int/9712006]; [solv-int/9506003].
13. S. M. Sergeev, V. V. Mangazeev and Yu. G. Stroganov, J. Stat. Phys. 82, 31 (1996).
14. S. M. Sergeev, V. V. Bazhanov and V. V. Mangazeev, Quantum Dilogarithm and Tetrahedron Equation, Preprint IHEP 95 - 129 (unpublished), S. Sergeev, In Proceedings of the 10th International Conference on Problems of Quantum Field Theory, ed. by D. V. Shirkov, D. I. Kazakov, A. A. Vladimirov, Publishing Department JINR (1996) ISBN 5-85165-455-4 p. 154-157.
15. S. M. Sergeev, V. V. Bazhanov and V. V. Mangazeev, Quantum Dilogarithm and Tetrahedron Equation, Preprint IHEP 95 - 129 (unpublished), S. Sergeev, In Proceedings of the 10th International Conference on Problems of Quantum Field Theory, ed. by D. V. Shirkov, D. I. Kazakov, A. A. Vladimirov, Publishing Department JINR (1996) ISBN 5-85165-455-4 p. 154-157.
16. V. Bazhanov, A. Bobenko and N. Reshetikhin, Commun. Math. Phys. 175, 377 (1996).
17. J.-M. Maillard and S. M. Sergeev, Phys. Lett. B405, 55 (1997).
18. S. M. Sergeev, On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation, [solv-int/9709013].
19. S. M. Sergeev, Phys. Lett. A253, 145 (1998).
20. S. M. Sergeev, J. Phys. A32, 5639 (1999).
21. S. M. Sergeev, in "Integrable Structures of Exactly Solvable Two-Dimensional Models etc.", eds. S. Pakuliak and G. von Gehlen, NATO Science Series II 35, (Kluwer, Dordrecht 2001), p. 293-304.
22. L. D. Faddeev and A. Yu. Volkov, Theoret. and Math. Phys. 92, 837 (1992).
23. L. D. Faddeev and R. M. Kashaev, Mod. Phys. Lett. A9, 427 (1994).
24. R. M. Kashaev, I. G. Korepanov and S. M. Sergeev, [solv-int/9801015].
25. V. V. Bazhanov and N. Yu. Reshetikhin, J. Phys. A28, 2217 (1995).
26. V. V. Bazhanov and N. Yu. Reshetikhin, "Chiral Potts model and discrete Sine-Gordon model at roots of unity", unpublished (1995).
27. S. M. Sergeev, Mod. Phys. Lett., A12, 1393 (1997).
28. S. M. Sergeev, Theoret. and Math. Phys. 118, 378 (1999); 124, 1187 (2000).
29. S. M. Sergeev, Theoret. and Math. Phys. 118, 378 (1999); 124, 1187 (2000).
30. V. V. Bazhanov and R. J. Baxter, J. Stat. Phys. 71, 839 (1993).
31. I. Krichever, Russian Math. Survey 33, 215 (1978).
32. T. Shitota, Inventione Mathematicae 83, 333 (1986).
33. M. Mulase, J. Diff. Geom. 19, 403 (1984).
34. I. Krichever, P. Wiegmann and A. Zabrodin, Commun. Math. Phys. 193, 373 (1998).
35. S. M. Sergeev, J. Nonlin. Math. Phys. 7, 57 (2000).
36. D. Mumford, Tata lectures on Theta I, II, Birkhauser (1983), (1985).
37. S. Sergeev, Functional equations and quantum separation of variables for 3D spin models, preprint MPIM 2002-46, available at http://www.mpim-bonn.mpg.de/ html-/library/library.html.
38. S. Pakuliak and S. Sergeev, Quantum relativistic Toda chain at root of unity: Isospectrality, modified Q-operator and functional Bethe ansatz, preprint MPIM 02-45.
39. G. von Gehlen, S. Pakuliak and S. Sergeev, J. Phys. A36, 975 (2003).
40. S. Pakuliak and S. Sergeev, Spectral curves and parameterizations of a discrete integrable 3-dimensional model, preprint MPIM 02-85.
41. S. Sergeev, An evidence for a phase transition in three dimensional lattice models, preprint MPIM 2002-139.
42. G. von Gehlen, S. Pakuliak and S. Sergeev, "Solutions of the tetrahedron equation", in preparation.