Ground-state properties of solid-on-solid models with disordered substrates

We study the glassy superrough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a minimum-cost-flow algorithm. Results for the height-height correlation function are compared with analytical and numerical predictions. The domain-wall energy of a boundary-induced step grows logarithmically with system size, indicating the marginal stability of the ground state, and the fractal dimension of the step is estimated. The sensibility of the ground state with respect to infinitesimal variations of the quenched disorder is analyzed.