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

Abstract

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 ρ}) in Fourier space, as a function of ρand 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 + ρ) are genuinely different which could lead to a re-interpretation of results in the literature.

Latex, 7 pages, eps files for two figures as well as Europhys. Lett. style files included; slightly expanded reincarnation

References in corpus (2)

• Quantized Scaling of Growing Surfaces
• Non-universal exponents in interface growth

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