Propagator for the wetting transition in 1+1 dimensions

Abstract

The partition function or propagator Z(${y}_{2}$,${y}_{1}$;${x}_{2}$-${x}_{1}$) of a solid-on-solid interface with fixed endpoints (${y}_{1}$,${x}_{1}$),(${y}_{2}$,${x}_{2}$), fluctuating in the half-plane y>0 with an attractive contact force at y=0, is evaluated in terms of elementary functions. Finite-size-scaling properties are discussed. Expressed in terms of rescaled position variables ${\ensuremath{\xi}}_{\ensuremath{\perp}}^{\mathrm{\ensuremath{-}}1}$y,${\ensuremath{\xi}}_{?}^{\mathrm{\ensuremath{-}}1}$x, the propagator appears to be a universal quantity. The scaling function for energy-energy correlations obtained by Ko and Abraham for the wetting transition in the two-dimensional Ising model is derived from the propagator. An analogous scaling function for spin-spin correlations is given. The shape of a droplet adjacent to the wall is studied as the temperature is lowered through the wetting temperature.