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.
A disordered fermion model defined on a two-dimensional square lattice with $\ensuremath{\pi}$ flux is studied. Time-reversal symmetry and one of four possible chiral symmetries are imposed. The continuum limit of the model near zero energy yields Dirac fermions with chiral symmetry. It is shown that one of them has $\mathrm{Sp}(n)\ifmmode\times\else\texttimes\fi{}\mathrm{Sp}(n)$ symmetry whereas others have U
(2n) symmetry, both of which are broken to Sp
(n), and the fluctuation around a saddle point is described, respectively, by the Sp
(n)2 Wess-Zumino-Witten model and U
(2n)/Sp
(n) nonlinear sigma model.