  Optimum ground states are constructed in two dimensions by using so called
vertex state models. These models are graphical generalizations of the
well-known matrix product ground states for spin chains. On the hexagonal
lattice we obtain a one-parametric set of ground states for a five-dimensional
manifold of S=3/2 Hamiltonians. Correlation functions within these ground
states are calculated using Monte-Carlo simulations. In contrast to the
one-dimensional situation, these states exhibit a parameter-induced second
order phase transition. In the disordered phase, two-spin correlations decay
exponentially, but in the Neel ordered phase alternating long-range
correlations are dominant. We also show that ground state properties can be
obtained from the exact solution of a corresponding free-fermion model for most
values of the parameter.
