  We study numerically the density profile in the six-vertex model with domain
wall boundary conditions. Using a Monte Carlo algorithm originally proposed by
Allison and Reshetikhin we numerically evaluate the inhomogeneous density
profiles in the disordered and antiferromagnetic regimes where frozen corners
appear. At the free fermion point we present an exact finite-size formula for
the density on the horizontal edges that relies on the imaginary time transfer
matrix approach. In all cases where exact analytic forms for the density and
the arctic curves are known the numerical method shows perfect agreement with
them. This also suggests the possibility of its use for accurate quantitative
purposes.
