Non-order parameter Langevin equation for a bounded Kardar-Parisi-Zhang universality class

TL;DR

This paper introduces a novel Langevin equation for a bounded KPZ universality class, describing the pinning-depinning transition with improved numerical accuracy and offering a new analytical approach.

Contribution

It presents a continuous Langevin equation with a non-order parameter field for the bounded KPZ class, complementing existing models and enabling advanced analytical studies.

Findings

Good agreement with microscopic models

Enhanced numerical precision

Provides a basis for further analytical work

Abstract

We introduce a Langevin equation describing the pinning-depinning phase transition experienced by Kardar-Parisi-Zhang interfaces in the presence of a bounding ``lower-wall''. This provides a continuous description for this universality class, complementary to the different and already well documented one for the case of an ``upper-wall''. The Langevin equation is written in terms of a field that is not an order-parameter, in contrast to standard approaches, and is studied both by employing a systematic mean-field approximation and by means of a recently introduced efficient integration scheme. Our findings are in good agreement with known results from microscopic models in this class, while the numerical precision is improved. This Langevin equation constitutes a sound starting point for further analytical calculations, beyond mean-field, needed to shed more light on this poorly understood universality class.