Eur. Phys. J. B 9, 491-511 (1999)
https://doi.org/10.1007/s100510050790

Exact results for the Kardar-Parisi-Zhang equation with spatially correlated noise^*

¹ Institut für Theoretische Physik III, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
² Institut für Theoretische Physik, Technische Universität München, 85747 Garching, Germany
³ Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435, USA
⁴ Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

Received: 5 August 1998
Published online: 15 June 1999

Abstract

We investigate the Kardar-Parisi-Zhang (KPZ) equation in d spatial dimensions with Gaussian spatially long-range correlated noise -characterized by its second moment -by means of dynamic field theory and the renormalization group. Using a stochastic Cole-Hopf transformation we derive exact exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension . Below the lower critical dimension, there is a line marking the stability boundary between the short-range and long-range noise fixed points. For , the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above , one has to rely on some perturbational techniques. We discuss the location of this stability boundary in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively.