Interfacial correlation function for adsorption on a disc

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 disc-like substrate. For large disc radii and for temperatures close to the wetting temperature of the corresponding planar substrate the expressions for the height–height 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.