Abstract
The Kardar-Parisi-Zhang equation for surface growth is analyzed in the regime where the nonlinear coupling constant is small. We present detailed calculations for the mean-square surface width in terms of the bare parameters of the equation. For surface dimension d\ensuremath{\le}2, this quantity is shown to obey crossover scaling. The case d=2 is marked by an exponentially slow crossover associated with the marginally unstable character of the linear theory. For dg2 a renormalization-group analysis in the one-loop approximation yields a logarithmic scaling form at the roughening transition between smooth and rough growth phases. The crossover behavior on either side of this transition is discussed.
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