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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 → ∞. However, for J s /J 1 the critical region is exponentially small and practically invisible to numerical studies. A distinct pre-asymptotic regime exists in which the transition displays firstorder 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.

Kayser [Phys. Rev. Lett. 56, 1831] has proposed that surface ionization provides the longrange force responsible for the wetting layers seen in the binary liquid mixture CS2+CH3NO2 on borosilicate glass substrates. We use scaling theory to find the equation of state for the near-critical mixtures, and then derive a free-energy functional for the wetting layer that incorporates surface ionization forces. This model includes critical adsorption effects and is well suited for calculations of wetting layers in the single-phase region. Within the uncertainties of the material properties, reflectivities of the glass-liquid interface derived from the theoretical concentration profiles do agree with experimental reflectivity values for wetting layers in the one-phase region. We confirm that surface ionization produces the dominant long-range force in CS2+ CH3NO2 on glass.