Casimir contribution to the interfacial Hamiltonian for 3D wetting

TL;DR

This paper derives an interfacial model for 3D wetting that includes a Casimir contribution, revealing significant effects on adsorption and critical behavior, and clarifying fluctuation effects near wetting transitions.

Contribution

The authors exactly derive the interfacial Hamiltonian for 3D wetting from a microscopic model, incorporating the Casimir effect, which was previously neglected.

Findings

Casimir term increases adsorption near first-order wetting transitions.

It alters the critical singularities of tricritical wetting.

Numerical renormalization group results agree with Ising model simulations.

Abstract

Previous treatments of three-dimensional (3D) short-ranged wetting transitions have missed an entropic or low temperature Casimir contribution to the binding potential describing the interaction between the unbinding interface and wall. This we determine by exactly deriving the interfacial model for 3D wetting from a more microscopic Landau-Ginzburg-Wilson Hamiltonian. The Casimir term changes the interpretation of fluctuation effects occurring at wetting transitions so that, for example, mean-field predictions are no longer obtained when interfacial fluctuations are ignored. While the Casimir contribution does not alter the surface phase diagram, it significantly increases the adsorption near a first-order wetting transition and changes completely the predicted critical singularities of tricritical wetting, including the non-universality occurring in 3D arising from interfacial fluctuations. Using the numerical renormalization group we show that, for critical wetting, the asymptotic regime is extremely narrow with the growth of the parallel correlation length characterised by an effective exponent in quantitative agreement with Ising model simulations, resolving a longstanding controversy.