Ground-State Roughness of the Disordered Substrate and Flux Lines in d  =  2

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux-line arrays in the presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using d  =  2 systems up to size 420², with a minimum of 2×10³ realizations at each size, we find very strong evidence for a ln²(L) super-rough state at low temperatures.