Interfacial correlation function for adsorption on a disc

TL;DR

This paper derives the effective Hamiltonian for interface fluctuations on a disc-shaped substrate near the wetting transition, analyzing correlation functions and scaling behaviors relevant to adsorption phenomena.

Contribution

It introduces a novel derivation of the interfacial correlation function for curved substrates within the Landau-Ginzburg-Wilson framework, focusing on disc geometries.

Findings

Correlation function expressions depend on disc radius and temperature.

Identification of relevant scaling regimes near the wetting transition.

Analysis of correlation angle variations with system parameters.

Abstract

Within the Landau-Ginzburg-Wilson approach we derive the effective Hamiltonian governing fluctuations of an interface between two phases, one of them adsorbed on a disclike substrate. For large disc radii and for temperatures close to the wetting temperature of the corresponding planar substrate the expressions for the hight-hight correlation function and the accompanying correlation angle are derived. Their dependence on the disc radius and the reduced temperature is discussed and the relevant scaling regimes are identified.