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Near-Equilibrium Dynamics of Crystalline Interfaces with Long-Range Interactions in 1+1 Dimensional Systems

The dynamics of a one-dimensional crystalline interface model with long-range interactions is investigated. In the absence of randomness, the linear response mobility decreases to zero when the temperature approaches the roughening transition from above, in contrast to a finite jump at the critical point in the Kosterlitz-Thouless (KT) transition. In the presence of substrate disorder, there exists a phase transition into a low-temperature pinning phase with a continuously varying dynamic exponent $z>1$. The expressions for the non-linear response mobility of a crystalline interface in both cases are also derived.