RENORMALIZATION-GROUP ANALYSIS OF THE ANISOTROPIC KARDAR-PARISI-ZHANG EQUATION WITH SPATIALLY CORRELATED NOISE

Abstract

We analyze the anisotropic Kardar-Parisi-Zhang equation in general substrate dimensions d' with spatially correlated noise, [eta(K,omega)] = 0 and [eta(K,omega)eta(K',omega')] = 2D (k)delta(d')(K+K')delta(omega+omega') where D(k) = D-o + D(rho)k(-2 rho), using the dynamic renormalization group (RG) method. When the signs of the nonlinear terms in parallel and perpendicular directions are opposite, a finite stable fixed point is found for d'< d'(c) = 2+2 rho within one-loop order. The roughening exponent alpha and the dynamic exponent z associated with the stable fixed point are determined as alpha = 2/3{rho - [(d' - 2)/2]}, and z = 2 - alpha. For d' > d'(c), the RG transformations flow to the fixed point of the weak-coupling limit, so that the dynamic exponent becomes z = 2.