Interfaces in a random medium and replica symmetry breaking

The authors develop a variational approach for studying interfaces and other manifolds in a disordered quenched medium. The method may be applied to problems which range from directed polymers to the interface of an Ising model in a random magnetic field. They find that replica symmetry is spontaneously broken and the results of the Flory approximation are recovered in a simple way. Corrections to this approximation may be computed in a systematic way.