Abstract
We combine an exact functional relation, the inversion relation, with conventional high-temperature expansions to explore the analytic properties of the anisotropic Ising model on both the square and simple cubic lattice. In particular, we investigate the nature of the singularities that occur in partially resummed expansions of the partition function and of the susceptibility.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. J. Baxter,Fundamental Problems in Statistical Mechanics V (Proceedings of the 1980 Enschede Summer School), E. G. D. Cohen, ed. (North-Holland, Amsterdam), 1980.
J. M. Maillard,J. Phys. (Paris) 46:329 (1985).
A. B. Zamolodchikov and A. B. Zamolodchikov,Ann. Phys. 120:253 (1979).
Y. G. Stroganov,Phys. Lett. 74A:116 (1979).
C. L. Schultz,Phys. Rev. Lett. 46:629 (1981).
S. V. Pokrovsky and Y. A. Bashilov,Commun. Math. Phys. 1982:103.
R. J. Baxter and P. A. Pearce,J. Phys. A 15:897 (1982).
M. T. Jaekel and J. M. Maillard,J. Phys. A 15:2241–2257 (1982).
M. T. Jaekel and J. M. Maillard,J. Phys. A 15:1309–1325 (1982).
C. Domb, inPhase Transitions and Critical Phenomena, Vol. 3, C. Domb and M. S. Green, eds. (Academic Press, 1974), pp. 357–484.
M. T. Jaekel and J. M. Maillard,J. Phys. A 16:1975 (1983).
J. Oitmaa, unpublished.
C. A. W. Citteur and P. W. Kasteleyn,Physica 62:17 (1972).
C. A. W. Citteur,Physica 64:415 (1973).
C. A. W. Citteur,Physica 66:94 (1973).
I. G. Enting, Ph. D. Thesis, Monash University (1974).
J. Oitmaa and I. G. Enting,J. Phys. C 5:231 (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hansel, D., Maillard, J.M., Oitmaa, J. et al. Analytical properties of the anisotropic cubic Ising model. J Stat Phys 48, 69–80 (1987). https://doi.org/10.1007/BF01010400
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01010400