Length scales for wetting transitions: Beyond the continuum Landau approximation for the interfacial binding potential

We show that the length scale α^-1, which appears in the interfacial binding potential of the effective Hamiltonian description of wetting transitions, should be identified with the ``true'' or exponential range of the pair-correlation function of the bulk (wetting) phase, rather than the Ornstein-Zernike (second-moment) bulk correlation length ξb. Since α^-1>ξb, this implies that the parameter {ω}=kBTα²/4{π}{Σ} ̃ \~{}{}, which determines the values of critical exponents for critical wetting in three dimensions, is significantly smaller than initial estimates of this quantity. For the simple-cubic Ising model ({α}ξb{)}^{{{-}}1}1.46 for T{T}R$, the roughening temperature, and depending on the magnitude of the interfacial stiffness {Σ} ̃ \~{}{}, we conclude {ω}{}0.5 is appropriate for such temperatures. We discuss the implications for recent Monte Carlo studies of critical wetting.