Ground-State Roughness of the Disordered Substrate and Flux Lines ind=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 $d=2\mathrm{}$ systems up to size ${420}^2$, with a minimum of $2\times {10}^3$ realizations at each size, we find very strong evidence for a ${ln}^2\left(L\right)$ super-rough state at low temperatures.