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The dynamics of a one-dimensional crystalline interface model with long-rangeinteractions is investigated. In the absence of randomness, the linear responsemobility decreases to zero when the temperature approaches the rougheningtransition from above, in contrast to a finite jump at the critical point inthe Kosterlitz-Thouless (KT) transition. In the presence of substrate disorder,there exists a phase transition into a low-temperature pinning phase with acontinuously varying dynamic exponent $z>1$. The expressions for the non-linearresponse mobility of a crystalline interface in both cases are also derived.Comment: 14 Pages, Revtex3.0, accepted to be published in Phys. Rev. E Rapid  Communicatio

Near-equilibrium dynamics of crystalline interfaces with long-range interactions in (1+1)-dimensional systems