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^−2ρ ) 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 (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.