Critical wetting of a class of nonequilibrium interfaces: A mean-field picture

TL;DR

This paper investigates critical wetting transitions of nonequilibrium interfaces using a mean-field approach, revealing distinct regimes depending on the KPZ nonlinearity sign and providing analytical and numerical solutions.

Contribution

It introduces a mean-field framework for nonequilibrium critical wetting, identifying three regimes for negative KPZ nonlinearity and solving them analytically.

Findings

Single Gaussian regime for positive KPZ nonlinearity

Three regimes for negative KPZ nonlinearity: Gaussian, weak-fluctuation, strong-fluctuation

Analytical solutions for strong-fluctuation regime using parabolic-cylinder functions

Abstract

A self-consistent mean-field method is used to study critical wetting transitions under nonequilibrium conditions by analyzing Kardar-Parisi-Zhang (KPZ) interfaces in the presence of a bounding substrate. In the case of positive KPZ nonlinearity a single (Gaussian) regime is found. On the contrary, interfaces corresponding to negative nonlinearities lead to three different regimes of critical behavior for the surface order-parameter: (i) a trivial Gaussian regime, (ii) a weak-fluctuation regime with a trivially located critical point and nontrivial exponents, and (iii) a highly non-trivial strong-fluctuation regime, for which we provide a full solution by finding the zeros of parabolic-cylinder functions. These analytical results are also verified by solving numerically the self-consistent equation in each case. Analogies with and differences from equilibrium critical wetting as well as nonequilibrium complete wetting are also discussed.