Stiffness instability in short-range critical wetting

Recent theoretical work has shown that an interface separating two fluid phases suffers changes in its (bare) effective stiffness, {Σ} ̃ \~{}{}(l)={Σ}̃ \~_∞+{Δ}{Σ} ̃ \~{}{}(l), when located at a distance l from a planar wall: terms varying as lᵏ{e}^{{{-}}j{{κ}}l}$ appear in {Δ}{Σ} ̃ \~{}{} (where 0{≤}k{≤}j=1,2, . . . and {κ} is the inverse bulk correlation length in the fluid wetting the wall). This may induce first-order wetting transitions when critical wetting had been expected. This general behavior of {Δ}{Σ} ̃ \~{}{}(l) is confirmed using an integral/adsorption constraint to determine l, in place of the original crossing constraint. The exact linearized functional renormalization-group technique is used to analyze the full wetting-phase diagram as a function of T, of {ω}=kB{T}cWκ²/4{π}{Σ} ̃ \~{}{}(TcW), and of q, the amplitude of the -le^-2κl term in {Δ}{Σ} ̃ \~{}{}. For dimensions d>3, any positive q (as generally expected) yields first-order wetting. The same is true for d=3 provided {ω}1/2; but when {ω}>1/2 nonclassical critical behavior is still found for small q〈qₜ({ω})〉0. Detailed expressions are obtained for 〈l〉, ξ_∥, etc., in the various critical and first-order regions. Numerical estimates show that previous Ising-model simulations probably encountered weakly first-order wetting transitions which might explain discrepancies with earlier renormalization-group predictions.