  We study the partition function per site of the integrable $Sp(2n)$ vertex
model on the square lattice. We establish a set of transfer matrix fusion
relations for this model. The solution of these functional relations in the
thermodynamic limit allows us to compute the partition function per site of the
fundamental $Sp(2n)$ representation of the vertex model. In addition, we also
obtain the partition function of vertex models mixing the fundamental with
other representations.
