Numerical investigation of the thermodynamic limit for ground states in models with quenched disorder

Numerical ground state calculations are used to study four models with quen ched disorder in finite samples with free boundary conditions. Extrapolatio n to the infinite volume limit indicates that the configurations in "window s" of fixed size converge to a unique configuration, up to global symmetrie s. The scaling of this convergence is consistent with calculations based on the fractal dimension of domain walls. These results provide strong eviden ce for the "two-state" picture of the low temperature behavior of these mod els. Convergence in three-dimensional systems can require relatively large windows.