Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
L\'eonie Canet, Hugues Chat\'e, Bertrand Delamotte, Nicol\'as Wschebor
TL;DR
This paper introduces a simplified non-perturbative renormalization group method for the KPZ equation, accurately capturing the phase diagram and strong-coupling behavior, with potential for systematic improvements.
Contribution
It provides a new approximation technique for the KPZ equation's renormalization group analysis that reproduces key physical features and suggests a change in behavior near four dimensions.
Findings
Correct phase diagram including strong-coupling phase
Reasonable scaling exponents in physical dimensions
Indications of a qualitative change near four dimensions
Abstract
We present a simple approximation of the non-perturbative renormalization group designed for the Kardar-Parisi-Zhang equation and show that it yields the correct phase diagram, including the strong-coupling phase with reasonable scaling exponent values in physical dimensions. We find indications of a possible qualitative change of behavior around . We discuss how our approach can be systematically improved.
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