A formula for the hopping expansion of 8-vertex models coupled to an external field

Abstract

We study a generalized 8-vertex model where the vertices are coupled to a locally varying field. We rewrite the partition function as an integral over Grassmann variables. In this form it is possible to explicitly evaluate all terms of the hopping expansion. Applications of the resulting formula, in particular its relation to 2-D lattice field theories with fermions are discussed.