Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho and the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the critical and correction-to-scaling exponents at the roughening transition are determined to all orders in a (d - d_c) expansion. We also argue that there is a intriguing possibility that the rough phases above and below the lower critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett. style files included; slightly expanded reincarnatio

Strongly anisotropic roughness in surfaces driven by an oblique particle flux

Using field theoretic renormalization, an MBE-type growth process with an obliquely incident influx of atoms is examined. The projection of the beam on the substrate plane selects a "parallel" direction, with rotational invariance restricted to the transverse directions. Depending on the behavior of an effective anisotropic surface tension, a line of second order transitions is identified, as well as a line of potentially first order transitions, joined by a multicritical point. Near the second order transitions and the multicritical point, the surface roughness is strongly anisotropic. Four different roughness exponents are introduced and computed, describing the surface in different directions, in real or momentum space. The results presented challenge an earlier study of the multicritical point.Comment: 11 pages, 2 figures, REVTeX

On Critical Exponents and the Renormalization of the Coupling Constant in Growth Models with Surface Diffusion

It is shown by the method of renormalized field theory that in contrast to a statement based on a mathematically ill-defined invariance transformation and found in most of the recent publications on growth models with surface diffusion, the coupling constant of these models renormalizes nontrivially. This implies that the widely accepted supposedly exact scaling exponents are to be corrected. A two-loop calculation shows that the corrections are small and these exponents seem to be very good approximations.Comment: 4 pages, revtex, 2 postscript figures, to appear in Phys.Rev.Let