Dynamical Renormalization Group Study for a Class of Non-local Interface Equations

Abstract

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, that agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent on the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems like the Lai-Das Sarma-Villain equation, in which vertex cancellation is known {\em not to} imply an associated symmetry of the equation.

34 pages, 9 figures. Journal of Statistical Mechanics: Theory and Experiments (in press)

References in corpus (14)

• A pseudo-spectral method for the Kardar-Parisi-Zhang equation
• Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation
• Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids
• Transients due to instabilities hinder Kardar-Parisi-Zhang scaling: a unified derivation for surface growth by electrochemical and chemical vapor deposition
• Pseudospectral versus finite-differences schemes in the numerical integration of stochastic models of surface growth
• Growing Surfaces with Anomalous Diffusion - Results for the Fractal Kardar-Parisi-Zhang Equation
• Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1+1 dimensions
• Unified moving boundary model with fluctuations for unstable diffusive growth
• Gauge fixing, BRS invariance and Ward identities for randomly stirred flows
• Generic equations for pattern formation in evolving interfaces
• Kinetic roughening in a realistic model of non-conserved interface growth
• Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation
• Thermal Re-emission Model
• Re-examination of the infra-red properties of randomly stirred hydrodynamics

Cited by in corpus (4)

• Universality of cauliflower-like fronts: from nanoscale thin films to macroscopic plants
• Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models
• Dimensional fragility of the Kardar-Parisi-Zhang universality class
• Strong anisotropy in two-dimensional surfaces with generic scale invariance: Non-linear effects