Upper Critical Dimension for Wetting in Systems with Long-Range Forces

Abstract

It is shown that the upper critical dimension $d^{*}$ for complete wetting is $d^{*}=3\mathrm{}$ for shortrange forces and $d^{*}<3\mathrm{}$ for long-range forces. The critical exponent ${\nu }_{\parallel }$ for the divergence of transverse correlations at complete wetting in three-dimensional systems is found to be ${\nu }_{\parallel }=\frac{1}{2}$ for short-range forces and ${\nu }_{\parallel }=\frac{2}{3}$ for long-range forces of van der Waals type.