Capillary-wave models and the effective average action scheme of functional renormalization group

TL;DR

This paper revisits the functional renormalization-group approach to wetting transitions, deriving a transparent truncation scheme applicable in any spatial dimension and analyzing the scheme dependence of the capillary parameter.

Contribution

It introduces a simple truncation of the exact flow equation for wetting transitions, clarifying approximations and exploring scheme dependence of key parameters.

Findings

The truncation reproduces standard RG theory of wetting transitions.

The capillary parameter omega is scheme-dependent below d=3.

Omega is robust at d=3 against scheme variations.

Abstract

We reexamine the functional renormalization-group theory of wetting transitions. As a starting point of the analysis we apply an exact equation describing renormalization group flow of the generating functional for irreducible vertex functions. We show how the standard nonlinear renormalization group theory of wetting transitions can be recovered by a very simple truncation of the exact flow equation. The derivation makes all the involved approximations transparent and demonstrates the applicability of the approach in any spatial dimension d\geq 2. Exploiting the non-uniqueness of the renormalization-group cutoff scheme, we find however, that the capillary parameter omega is a scheme-dependent quantity below d=3. For d=3 the parameter omega is perfectly robust against scheme variation.