  The effect of open boundary conditions for four models with quenched disorder
are studied in finite samples by numerical ground state calculations.
Extrapolation to the infinite volume limit indicates that the configurations in
``windows'' of fixed size converge to a unique configuration, up to global
symmetries. The scaling of this convergence is consistent with calculations
based on the fractal dimension of domain walls. These results provide strong
evidence for the ``two-state'' picture of the low temperature behavior of these
models. Convergence in three-dimensional systems can require relatively large
windows.
