Abstract
The partition function of the Ising antiferromagnet is proved to have no zeroes in an annulus around the origin in the complexz-plane. The intersection of this annulus with the positive real axis belongs to the antiferromagnetic region. The free energy and the correlation functions are analytic in the annulus.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Minlos, R. A., Sinai, Ja. G.: Trudy Moskov. Mat. Obšč.17, 213–242 (1967); English translation: Trans. Moscow Math. Soc.17, 237–267 (1967).
Minlos, R. A., Sinai, Ja. G.: Trudy Moskov. Mat. Obšč.19, 113–178 (1968); English translation: Trans. Moscow Math. Soc.19, 121–196 (1968).
Dobrušin, R. L.: Funkcional. Anal. i Priložen.2, 44–57 (1968). English translation: Func. Anal. and Appl.2, 302 (1968).
Di Liberto, F.: Commun. math. Phys.29, 293–311 (1973)
Fortuin, C. M., Kasteleyn, P. W., Ginibre, J.: Commun. math. Phys.22, 89–103 (1971).
Lebowitz, J. L.: Phys. Lett.36A, 99–100 (1971).
Suzuki, M., Kawabata, C., Ono, S., Karaki, Y., Ikeda, M.: J. Phys. Soc. Japan29, 837–844 (1970).
Katsura, S., Abe, Y., Yamamoto, M.: J. Phys. Soc. Japan30, 347–357 (1971).
Ruelle, D.: Statistical Mechanics. New York: Benjamin 1969.
Author information
Authors and Affiliations
Additional information
On leave of absence from the University of Groningen, the Netherlands; supported by the Netherlands Organization for Pure Scientific Research (Z.W.O.).
Supported by the National Swiss Foundation for Scientific Research.
Rights and permissions
About this article
Cite this article
Brascamp, H.J., Kunz, H. Analyticity properties of the Ising model in the antiferromagnetic phase. Commun.Math. Phys. 32, 93–106 (1973). https://doi.org/10.1007/BF01645649
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01645649