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 quenched disorder in finite samples with free boundary conditions. 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.