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

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

1998-07-06

arxiv.org/abs/cond-mat/9807087v2

Europhys. Lett. 47 (1999) 14

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1209/epl/i1999-00343-4

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.

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