Abstract
Given an Ising antiferromagnet on a lattice with an AB substructure (bipartite lattice), one can consider the associated ferromagnet in which all the exchange constants are negated. Suppose the ferromagnet is above its critical temperature in the sense that there is an arc (−θ, θ) of the unit circle on which the partition function has no zeros in z = exp(2βH). We prove that the original antiferromagnet partition function will have no zeros in z in the disc orthogonal to the unit disc and passing through the two end points of the arc. In other words, the antiferromagnet free energy is analytic in the magnetic field for small fields.
Work supported by National Science Foundation Grant GP 26526
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Reference
H.J. Borchers, Nuovo Cimento 19, 787 (1961).
V. Glaser and J. Bros, “L’envelope d’holomorphie de I’union de deux polycercles,” CERN preprint (1961).
T.D. Lee and C.N. Yang. Phys. Rev. 87, 410 (1952).
S.Bochner and W.T. Martin, Several Complex Variables (Princeton U.P., Princeton, N.J., 1948).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1972 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lieb, E.H., Ruelle, D. (1972). A Property of Zeros of the Partition Function for Ising Spin Systems. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Statistical Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10018-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-662-10018-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-06092-2
Online ISBN: 978-3-662-10018-9
eBook Packages: Springer Book Archive