Numerical study of the disorder-driven roughening transition in an elastic manifold in a periodic potential

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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 continuous transition with a set of numerically estimated critical exponents that we compare with analytic results and those for a periodic elastic medium.