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A theory for surface transitions in the presence of a disordered pinningpotential is presented. Arbitrary disorder correlations are treated in theframework of a dynamical functional renormalization group. The rougheningtransition, where surface roughness and mobility behave discontinuously, isshown to turn smoothly into the continuous superroughening transition, when therange of disorder correlations is decreased. Implications for random-field$XY$-models and vortex glasses are discussed.Comment: 13 pages with 2 figures, latex+revte

Crystal Surfaces with Correlated Disorder: Phase Transitions between Roughening and Super-roughening