Exact solution of the six-vertex model with domain wall boundary conditions. Disordered phase

Communications in Mathematical Physics

Volumn 268, Issue 1, 2006, Pages 223-284

  Bleher, Pavel M ^a   Fokin, Vladimir V ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749345985     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0097-y     Document Type: Article

References (29)

1. Baxter, R.: Exactly solved models in statistical mechanics. San Diego, CA: Academic Press
2. Batchelor, M.T., Baxter, R.J., O'Rourke, M.J., Yung, C.M.: Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions. J. Phys. A 28, 2759-2770 (1995)
3. Bleher, P., Its, A.: Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. Math. 150, 185-266 (1999)
4. Bleher, P., Its, A.: Double scaling limit in the random matrix model: the Riemann-Hilbert approach. Commun. Pure Appl. Math. 56, 433-516 (2003)
5. Bleher, P., Its, A.: Asymptotics of the partition function of a random matrix model. Ann. Inst. Fourier 55, 1943-2000 (2005)
6. Bogoliubov, N.M., Kitaev, A.M., Zvonarev, M.B.: Boundary polarization in the six-vertex model. Phys. Rev. E 65, 026126 (2002)
7. Bressoud, D.M.: Proofs and confirmations. The story of the alternating sign matrix conjecture, MAA, Cambridge University Press, Cambridge, 1999
8. Colomo, F., Pronko, A.G.: Square ice, alternating sign matrices, and classical orthogonal polynomials, J. Stat. Mech. Theory Exp. no. 1, 005, 2005 33 pp. (electronic)
9. Deift, P.A., Kriecherbauer, T., McLaughlin, K.T-R.: New results on equilibrium measure for logarithmic potentials in the presence of an external field. J. Approx. Theory 95, 388-475 (1998)
10. Deift, P.A., Kriecherbauer, T., McLaughlin, K.T-R., Venakides, S., Zhou, Z.: Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Commun. Pure Appl. Math. 52, 1335-1425 (1999)
11. Ercolani, N.M., McLaughlin, K.T.-R.: Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques and applications to graphical enumeration. Int. Math. Res. Not. 14, 755-820 (2003)
12. Izergin, A.G., Partition function of the six-vertex model in a finite volume. Sov. Phys. Dokl. 32, 878 (1987)
13. Izergin, A.G., Coker, D.A., Korepin, V.E.: Determinant formula for the six-vertex model. J. Phys. A 25, 4315 (1992)
14. Korepin, V.E.: Calculation of norms of Bethe wave functions. Commun. Math. Phys. 86, 391-418 (1982)
15. Korepin, V., Zinn-Justin, P.: Thermodynamic limit of the six-vertex model with domain wall boundary conditions. J. Phys. A 33(40), 7053 (2000)
16. Kriecherbauer, T., McLaughlin, K.T-R.: Strong asymptotics of polynomials orthogonal with respect to Freud weights. Int. Math. Res. Not. 6, 299-333 (1999)
17. Kuperberg, G.: Another proof of the alternating sign matrix conjecture. Int. Math. Res. Not. 3, 139-150 (1996)
18. Lieb, E.H.: Exact solution of the problem of the entropy of two-dimensional ice. Phys. Rev. Lett. 18, 692 (1967)
19. Lieb, E.H.: Exact solution of the two-dimensional Slater KDP model of an antiferroelectric. Phys. Rev. Lett. 18, 1046-1048 (1967)
20. Lieb, E.H.: Exact solution of the two-dimensional Slater KDP model of a ferroelectric. Phys. Rev. Lett. 19, 108-110 (1967)
21. Lieb, E.H.: Residual entropy of square ice. Phys. Rev. 162, 162 (1967)
22. Lieb, E.H., Wu, F.Y.: Two dimensional ferroelectric models. In: Phase Transitions and Critical Phenomena. Domb, C., Green M. (eds), Vol. 1, London: Academic Press, 1972, pp. 331-490
23. Mills, W.H., Robbins, D.P., Rumsey, H.: Proof of the Macdonald conjecture. Invent. Math. 66, 73-87 (1982)
24. Mills, W.H., Robbins, D.P., Rumsey, H.: Alternating-sign matrices and descending plane partitions. J. Combin. Theory, Ser. A 34, 340-359 (1983)
25. Sogo, K.: Toda molecule equation and quotient-difference method. J. Phys. Soc. Japan 62, 1887 (1993)
26. Szego, G.: Orthogonal Polynomials. Fourth edition. Colloquium Publications, Vol. 23, Providence, RI: AMS, 1975
27. Sutherland, B.: Exact solution of a two-dimensional model for hydrogen-bonded crystals. Phys. Rev. Lett. 19, 103-104 (1967)
28. Zeilberger, D.: Proof of the alternating sign matrix conjecture. New York J. Math. 2, 59-68 (1996)
29. Zinn-Justin, P.: Six-vertex model with domain wall boundary conditions and one-matrix model. Phys. Rev. E 62, 3411-3418 (2000)