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

We show that the length scale ${\mathrm{\alpha }}^{\mathrm{-}1}$, 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 ${\xi }_{\mathit{b}}$. Since ${\mathrm{\alpha }}^{\mathrm{-}1}$>${\xi }_{\mathit{b}}$, this implies that the parameter ω=${\mathit{k}}_{\mathit{B}}$T${\mathrm{\alpha }}^2$/4πΣ̃, 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${\xi }_{\mathit{b}}$${)}^{\mathrm{-}1}$≊1.46 for T≳${\mathit{T}}_{\mathit{R}}$, the roughening temperature, and depending on the magnitude of the interfacial stiffness Σ̃, we conclude ω≲0.5 is appropriate for such temperatures. We discuss the implications for recent Monte Carlo studies of critical wetting.