Comment on simple scaling theory for three-dimensional critical wetting with short-ranged forces

The scaling theory used to analyze the results of recent Monte Carlo simulations of a three-dimensional critical wetting transition is reexamined. It is shown that the scaling form of the surface-layer susceptibility ${\chi }_1$ suggested in the earlier analyses is not always consistent with an exact thermodynamic requirement. A consistent scaling form for ${\chi }_1$ is introduced and used to derive relationships between the thickness of the wetting film $l$, the transverse correlation length ${\xi }_{\parallel }$, and the surface roughness ${\xi }_{\perp }$. These relationships are consistent with the results of renormalization-group calculations. The present procedure avoids introducing specific (nontrivial) corrections to the standard scaling ansatz for the singular contribution to the surface excess free energy.