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

¹ 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

Received: 20 April 1999
Accepted: 28 April 1999

Abstract

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.