  The global phase diagram of wetting in the two-dimensional (2d) Ising model
is obtained through exact calculation of the surface excess free energy.
Besides a surface field for inducing wetting, a surface-coupling enhancement is
included. The wetting transition is critical (second order) for any finite
ratio of surface coupling J_s to bulk coupling J, and turns first order in the
limit J_s/J to infinity. However, for J_s/J much larger than 1 the critical
region is exponentially small and practically invisible to numerical studies. A
distinct pre-asymptotic regime exists in which the transition displays
first-order character. Surprisingly, in this regime the surface susceptibility
and surface specific heat develop a divergence and show anomalous scaling with
an exponent equal to 3/2.
