LENGTH SCALES FOR WETTING TRANSITIONS - BEYOND THE CONTINUUM LANDAU APPROXIMATION FOR THE INTERFACIAL BINDING POTENTIAL

We show that the length scale alpha-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(b). Since alpha(-1) > xi(b), this implies that the parameter omega = K(B) T-alpha(2)/4-pi-SIGMA approximately, 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 (alpha-xi(b))-1 almost-equal-to 1.46 for T greater-than-or-similar-to T(R), the roughening temperature, and depending on the magnitude of the interfacial stiffness SIGMA approximately, we conclude omega less-than-or-similar-to 0.5 is appropriate for such temperatures. We discuss the implications for recent Monte Carlo studies of critical wetting.