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, Σ̃(l)=Σ${\mathrm{̃}}_{\mathrm{\infty }}$+ΔΣ̃(l), when located at a distance l from a planar wall: terms varying as ${\mathit{l}}^{\mathit{k}}$ ${\mathit{e}}^{\mathrm{-}\mathit{j}\mathrm{\kappa }\mathit{l}}$ appear in ΔΣ̃ (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 ΔΣ̃(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=${\mathit{k}}_{\mathit{B}}$ ${\mathit{T}}_{\mathit{c}\mathit{W}}$ ${\mathrm{\kappa }}^2$/4πΣ̃(${\mathit{T}}_{\mathit{c}\mathit{W}}$), and of q, the amplitude of the -${\mathit{le}}^{\mathrm{-}2\mathrm{\kappa }\mathit{l}}$ term in ΔΣ̃. For dimensions d>3, any positive q (as generally expected) yields first-order wetting. The same is true for d=3 provided ω1/2 nonclassical critical behavior is still found for small q〈${\mathit{q}}_{\mathit{t}}$(ω)〉0. Detailed expressions are obtained for 〈l〉, ${\xi }_{\mathrm{\parallel }}$, 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.