Abstract
The exact solution of the asymmetric six-vertex model is cast in an algebraically simple form in which the extraction of physical quantities is transparent. This is used to derive a symmetry relation corresponding to the exchange of spatial x and y axes. As an application we study the field-induced phase transition of a two-dimensional analogue of spin ice, a frustrated Ising magnet.
Similar content being viewed by others
REFERENCES
E. H. Lieb, Phys. Rev. Lett. 18:692 (1967); 18:1046 (1967).
B. Sutherland, Phys. Rev. Lett. 19:103 (1967).
E. H. Lieb, Phys. Rev. Lett. 19:108 (1967).
C. P. Yang, Phys. Rev. Lett. 19:586 (1967); B. Sutherland, C. N. Yang, and C. P. Yang, Phys. Rev. Lett. 19:588 (1967).
E. H. Lieb and F. Y. Wu, in Phase Transitions and Critical Phenomena, Vol. 1, C. Domb and M. S. Green, eds. (Academic Press, London, 1972).
R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1972).
I. M. Nolden, J. Stat. Phys. 67:155 (1992).
I. M. Nolden and H. van Beijeren, Phys. Rev. B 49:17224 (1994).
M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske, and K. W. Godfrey, Phys. Rev. Lett. 79:2554 (1997).
R. Moessner, Phys. Rev. B 57:R5587 (1998).
S. T. Bramwell and M. J. Harris, J. Phys.: Condens. Matter 10:L215 (1998).
M. J. Harris, S. T. Bramwell, P. C. W. Holdsworth, and J. D. M. Champion, Phys. Rev. Lett., in press (1998).
D. J. Bukman and J. D. Shore, J. Stat. Phys. 78:1277 (1995).
H. Y. Huang, F. Y. Wu, H. Kunz, and D. Kim, Physica A 228:1 (1996).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Watson, G.I. Symmetry Relations for the Six-Vertex Model. Journal of Statistical Physics 94, 1045–1054 (1999). https://doi.org/10.1023/A:1004547503489
Issue Date:
DOI: https://doi.org/10.1023/A:1004547503489