Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation

TL;DR

This paper investigates the anisotropic KPZ equation using nonperturbative renormalization group methods, revealing the stability of the isotropic rough phase and identifying a new anisotropic strong coupling fixed point at non-integer dimensions.

Contribution

It provides a nonperturbative analysis showing the stability of the isotropic phase and discovers a novel anisotropic fixed point in the strong coupling regime.

Findings

Isotropic strong coupling fixed point is always stable.

Anisotropic strong coupling fixed point exists for opposite sign nonlinear couplings.

Stability results hold across non-integer dimensions.

Abstract

We study the anisotropic Kardar-Parisi-Zhang equation using nonperturbative renormalization group methods. In contrast to a previous analysis in the weak-coupling regime we find the strong coupling fixed point corresponding to the isotropic rough phase to be always locally stable and unaffected by the anisotropy even at non-integer dimensions. Apart from the well-known weak coupling and the now well established isotropic strong coupling behavior, we find an anisotropic strong coupling fixed point for nonlinear couplings of opposite signs at non-integer dimensions.