Improved Perturbation Theory for the Kardar-Parisi-Zhang Equation

TL;DR

This paper introduces improved variational perturbation schemes for the KPZ equation to better estimate the dynamic exponent z, achieving closer alignment with numerical simulations in low dimensions but still predicting z=2 at a critical dimension.

Contribution

It develops and applies variationally improved perturbation methods for the KPZ equation, offering more accurate estimates of the dynamic exponent compared to previous self-consistent approaches.

Findings

Better agreement with numerical simulations in low dimensions.

Consistent broad features across different schemes.

Predicts z=2 at a critical dimension, conflicting with simulations.

Abstract

We apply a number of schemes which variationally improve perturbation theory for the Kardar-Parisi-Zhang equation in order to extract estimates for the dynamic exponent z. The results for the various schemes show the same broad features, giving closer agreement with numerical simulations in low dimensions than self-consistent methods. They do, however, continue to predict that z=2 in some critical dimension d_c in disagreement with the findings of simulations.