Universality in two-point functions at wetting: Exact scaling function for energy-density correlations

The scaling function at the wetting transition for the two-point energy-density correlation function is computed exactly for two-dimensional Ising models with interfaces in the [10] and [11] directions. The two-point separations perpendicular and parallel to the wall are scaled by ξ_⊥~(Tw-T)^-1 and ξ_∥~(Tw-T)^-2, respectively; and the energy-density operator scales as Tw-T. The resulting scaling function is independent of the microscopic couplings, boundary interactions, wall orientation, and specifics of the operator. Furthermore, the result is simple and consists of Gaussians and error functions, suggestive of random walk.