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

TL;DR

The paper derives an explicit hopping expansion formula for a generalized 8-vertex model coupled to a local field, connecting it to 2D lattice fermion theories.

Contribution

It provides a new explicit formula for the hopping expansion of 8-vertex models with external fields, expressed via Grassmann integrals.

Findings

Explicit evaluation of hopping expansion terms

Connection to 2D lattice fermion theories

Potential applications in statistical and quantum field theories

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.