Auxiliary matrices on both sides of the equator

Korff, C. (2005) Auxiliary matrices on both sides of the equator. Journal of Physics A: Mathematical and General, 38(1), pp. 47-67. (doi:10.1088/0305-4470/38/1/003)

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Publisher's URL: http://dx.doi.org/10.1088/0305-4470/38/1/003

Abstract

The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity and an odd number of sites the eigenvalues contain two linear independent solutions to Baxter's TQ-equation corresponding to the Bethe ansatz equations above and below the equator. In contrast, one finds for even spin-chains only one linear independent solution and complete strings. The other main result is the proof of a previous conjecture on the degeneracies of the six-vertex model at roots of unity. The proof rests on the derivation of a functional equation for the auxiliary matrices which is closely related to a functional equation for the eight-vertex model conjectured by Fabricius and McCoy.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Korff, Dr Christian
Authors: Korff, C.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Physics A: Mathematical and General
Publisher:Institute of Physics Publishing Ltd.
ISSN:0305-4470

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