  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.
