Analytic theory of the eight-vertex model

Details Analytic theory of the eight-vertex model Analytic theory of the eight-vertex model

2006-09-22

arxiv.org/abs/hep-th/0609153v3

Nucl.Phys.B775:225-282,2007

Physics

High Energy Physics

High Energy Physics - Theory

58 pages, 12 figures, minor corrections

Scientific paper

10.1016/j.nuclphysb.2006.12.021

We observe that the exactly solved eight-vertex solid-on-solid model contains an hitherto unnoticed arbitrary field parameter, similar to the horizontal field in the six-vertex model. The parameter is required to describe a continuous spectrum of the unrestricted solid-on-solid model, which has an infinite-dimensional space of states even for a finite lattice. The introduction of the continuous field parameter allows us to completely review the theory of functional relations in the eight-vertex/SOS-model from a uniform analytic point of view. We also present a number of analytic and numerical techniques for the analysis of the Bethe Ansatz equations. It turns out that different solutions of these equations can be obtained from each other by analytic continuation. In particular, for small lattices we explicitly demonstrate that the largest and smallest eigenvalues of the transfer matrix of the eight-vertex model are just different branches of the same multivalued function of the field parameter.

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