Renormalization group analysis of the anisotropic Kardar-Parasi-Zhang equation with spatially correlated noise

Abstract

We analyze the anisotropic Kardar-Parisi-Zhang equation in general substrate dimensions $d^{\prime }$ with spatially correlated noise, $⟨\tilde{\eta }(\mathbf{k},\omega )⟩=0$ and $⟨\tilde{\eta }(\mathbf{k},\omega )\tilde{\eta }({\mathbf{k}}^{\prime },{\omega }^{\prime })⟩$ $=2D(k){\delta }^{d^{\prime }}(\mathbf{k}+{\mathbf{k}}^{\prime })\delta (\omega +{\omega }^{\prime })$ where $D(k)=D_0+D_{\rho }{k}^{-2\rho }$, using the dynamic renormalization group (RG) method. When the signs of the nonlinear terms in parallel and perpendicular directions are opposite, a novel finite stable fixed point is found for $d^{\prime }<d_c^{\prime }\equiv 2+2\rho$ within one-loop order. The roughening exponent $\alpha$ and the dynamic exponent $z$ associated with the stable fixed point are determined as $\alpha =\frac{2}{3}(\rho -\frac{d^{\prime }-2}{2})$, and $z=2-\alpha$. For $d^{\prime }>d_c^{\prime }$, the RG transformations flow to the fixed point of the weak-coupling limit, so that the dynamic exponent becomes $z=2$.

arXiv comment10 pages, latex, one compressed uuencoded figure appended

References in corpus (1)

• Dynamics of Toom interface in three dimensions

Cited by in corpus (2)

• Faceted patterns and anomalous surface roughening driven by long-term correlated noise
• Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation