  The mixed spin-1/2 and spin-3/2 Ising model on the union jack lattice is
solved by establishing a mapping correspondence with the eight-vertex model. It
is shown that the model under investigation becomes exactly soluble as a
free-fermion eight-vertex model when the parameter of uniaxial single-ion
anisotropy tends to infinity. Under this restriction, the critical points are
characterized by critical exponents from the standard Ising universality class.
In a certain subspace of interaction parameters, which corresponds to a
coexistence surface between two ordered phases, the model becomes exactly
soluble as a symmetric zero-field eight-vertex model. This surface is bounded
by a line of bicritical points having interaction-dependent critical exponents
that satisfy a weak universality hypothesis.
