  The partition function of the six-vertex model on a square lattice with
domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix
model or a discretized version of it (similar to sums over Young diagrams),
depending on the phase. The expression is exact for finite lattice size, which
is equal to the size of the corresponding matrix. In the thermodynamic limit,
the matrix integral is computed using traditional matrix model techniques, thus
providing a complete treatment of the bulk free energy of the six-vertex model
with DWBC in the different phases. In particular, in the anti-ferroelectric
phase, the bulk free energy and a subdominant correction are given exactly in
terms of elliptic theta functions.
