KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables

TL;DR

This paper uses Non-perturbative Functional Renormalization Group methods to study the KPZ equation with spatially correlated noise, revealing how microscopic noise correlations influence non-universal observables while universal large-scale behavior remains unchanged.

Contribution

The study provides a detailed RG analysis of KPZ with correlated noise, connecting microscopic noise features to large-scale universal properties and non-universal observables.

Findings

Universal KPZ physics emerges at large scales regardless of noise correlation range.

Non-universal amplitude of the kinetic energy spectrum depends on microscopic noise correlations.

Results agree with previous numerical and analytical approaches, confirming the crossover behavior.

Abstract

We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $\xi$. We employ Non-perturbative Functional Renormalization Group methods in order to resolve the properties of the system at all scales. We show that the physics of the standard (uncorrelated) KPZ equation emerges on large scales independently of $\xi$. Moreover, the Renormalization Group flow is followed from the initial condition to the fixed point, that is from the microscopic dynamics to the large-distance properties. This provides access to the small-scale features (and their dependence on the details of the noise correlations) as well as to the universal large-scale physics. In particular, we compute the kinetic energy spectrum of the stationary state as well as its non-universal amplitude. The latter is experimentally accessible by measurements at large scales and retains a signature of the microscopic noise correlations. Our results are compared to previous analytical and numerical results from independent approaches. They are in agreement with direct numerical simulations for the kinetic energy spectrum as well as with the prediction, obtained with the replica trick by Gaussian variational method, of a crossover in $\xi$ of the non-universal amplitude of this spectrum.