Phys. Rev. A 45, 7156–7161 (1992)Kinetic surface roughening. I. The Kardar-Parisi-Zhang equation in the weak-coupling regimeReceived 28 August 1991; published in the issue dated May 1992 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≤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 d>2 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. © 1992 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.45.7156
DOI:
10.1103/PhysRevA.45.7156
PACS:
05.40.+j, 64.60.Ht, 68.55.-a, 68.10.Jy
See AlsoSee Also: Lei-Han Tang, Bruce M. Forrest, and Dietrich E. Wolf, Kinetic surface roughening. II. Hypercube-stacking models, Phys. Rev. A 45, 7162 (1992). |
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