Propagator for the wetting transition in 1+1 dimensions

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 ${\xi }_{\perp }^{\mathrm{-}1}$y,${\xi }_{?}^{\mathrm{-}1}$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.