Derivation of a Non-Local Interfacial Hamiltonian for Short-Ranged Wetting II: General Diagrammatic Structure

TL;DR

This paper extends the derivation of a non-local interfacial Hamiltonian for short-ranged wetting by incorporating higher-order interactions and diagrammatic methods, revealing long-range many-body effects and boundary condition influences.

Contribution

It introduces a general diagrammatic structure for the binding potential functional beyond the double-parabola approximation, accounting for cubic and quartic interactions.

Findings

Cubic and quartic interactions modify diagram coefficients.

Non-locality induces long-range many-body interfacial interactions.

Alternative boundary conditions and tricritical wetting are analyzed.

Abstract

In our first paper, we showed how a non-local effective Hamiltionian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Green's function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zig-zag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed.