  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.
