Volume 47, Number 1, July 1999
|Page(s)||14 - 20|
|Published online||01 September 2002|
Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
Lyman Laboratory of Physics, Harvard University
Cambridge, MA 02138, USA
2 Institut für Theoretische Physik, Technische Universität München James-Franck-Straße, 85747 Garching, Germany
3 Department of Physics, Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0435, USA
4 Institut für Theoretische Physik III, Heinrich-Heine-Universität 40225 Düsseldorf, Germany
Accepted: 28 April 1999
We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator in Fourier space, as a function of ρ 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 expansion. We also argue that there is a intriguing possibility that the rough phases above and below the lower critical dimension are genuinely different which could lead to a re-interpretation of results in the literature.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Ht – Dynamic critical phenomena
© EDP Sciences, 1999
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