Nonuniversalνfrom a van der Waals Theory of the Wetting Transition

On the basis of a van der Waals theory of wetting, we propose an asymptotic method by which the surface free energy can be studied analytically as a function of large coverage. In this Letter zeroth-order results for the exponential model are given, but higher-order terms will not alter the qualitative conclusions. We establish new results on the order of the wetting transition, and find a nonuniversal critical exponent, $\nu$, for the parallel correlation length.