We investigate the roughening phase transition of a $(3+1)$-dimensional elastic manifold driven by the completion between a periodic pinning potential and a randomly distributed impurities. The elastic manifold is modeled by a solid-on-solid type interface model, and universal features of the transition from a flat phase (for strong periodic potential) to a rough phase (for strong disorder) are studied at zero temperature using a combinatorial optimization algorithm technique. We find a { \it continuous} transition with a set of numerically estimated critical exponents that we compare with analytic results and those for a periodic elastic medium.
Categories: cond-mat.stat-mech cond-mat.dis-nn