Solution of Eight-vertex Lattice Model Without Elliptic Functions

Abstract

Baxter's method of solving the eight-vertex model in lattice statistical mechanics is examined from an elementary point of view. It is shown that the algebraic operations in the method can be carried out without recourse to elliptic functions. These include: construction of certain subspaces invariant uti.der the action of the transfer matrix; reduction of the transfer matrix eigenvalue problem to an equivalent ice-type problem and construction of certain matrices which commute with the transfer matrix and satisfy a functional matrix equation.