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Functional relations in the eight - vertex model

Vladimir V. Bazhanov

Published Aug 8, 2007• 0 citations
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Abstract

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.

DOI
10.22323/1.038.0001

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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.
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The continuous limit of the eight-vertex model is shown to give solely the Massive Thirring Model (MTM). More precisely, using the light-cone lattice approach we find a whole class of lattice spacing (a) dependences in the eight vertex parameters (θ, γ, k) yielding a relative field theory in the a=0 limit. This turns out to be the MTM with no dependence on k. The exact excitation spectrum calculation presented here lead to these conclusions. Analogous results are reached from a perturbative renormalization group study of the anisotropic current-current continuum fermion field theory.
It is shown that a proper analytic continuation of eigenvalues of a special inhomogeneous eight-vertex system determines the "phases" and the spectrum of a one-dimensional fermion gas model, and thus provides a particular example of the long suspected connection between factorized SSS matrices and lattice statistical systems.