On the partition function of the Sp(4) integrable vertex model

Abstract

In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under Sp(4) symmetry. We establish a set of functional relations which include a transfer matrix inversion identity. The solution of these relations in the thermodynamic limit allows us to compute the partition function per site of the fundamental Sp(4) representation of the vertex model. As a byproduct we also obtain the partition function per site of a vertex model mixing the four and five dimensional representations of the Sp(4) symmetry.