A universal parameterization of finite-size effects for interfaces in two dimensions, conformal mappings and local scale invariance

Abstract

The author shows that all equilibrium statistical properties of an interface confined in a strip geometry, with arbitrary aspect ratio, exactly at a second-order, fluctuation dominated, interfacial unbinding (wetting) transition are determined by a single number q for interfacial binding potentials that are conformally mapped from the semi-infinite plane. The parameter q distinguishes the fluctuation regimes describing the wetting transition and can be directly related to wetting critical exponents. In the strong-fluctuation regime one finds q=0 whilst in the weak-fluctuation regime q=1. The values of q at all intermediate-fluctuation scaling regimes are also determined. He shows that the eigenstates of the transfer differential operator for conformally mapped marginal long-ranged potentials are the simplest possible generalization of the eigenstates corresponding to systems with short-ranged forces. He speculates that the universal parametrization of the finite-size effects at fluctuation dominated wetting transitions is a consequence of local scale invariance.