EFFECTIVE INTERFACE HAMILTONIANS FOR SHORT-RANGE CRITICAL WETTING

The derivation of effective interface Hamiltonians on the basis of an underlying noncritical bulk order-parameter theory is critically examined for use in studying critical wetting transitions in (d = 3)-dimensional systems with short-range forces. A crossing constraint on the interfacial profile is used to define the fluctuating interface location l(y) and exact general expressions are obtained for the effective wall-interface potential W[l(y)] and for the wall-modified interfacial stiffness SIGMA [l(y)] in terms of a constrained planar order-parameter profile. Previous discussions in the literature are shown to be inadequate. Explicit formulas for W and SIGMA are obtained when the bulk thermodynamic potential for the wetting-layer-phase is purely parabolic. Novel terms varying as le(-jkappal) (j = 2,3,...) appear in the decay of SIGMA(l) to the free-interface limit SIGMA(infinity); here, 1/kappa = xi(beta) is the true correlation length of the bulk wetting-layer phase. General nonparabolic bulk potentials are analyzed perturbatively, leading to terms in W(l) decaying as w(jk)l(k)e(-jkappal) for 0 less-than-or-equal-to k less-than-or-equal-to j = 1, 2,.... An alternative, generalized adsorption definition for l(y) can be solved exactly for a phi4 bulk potential and yields closely similar results for W(l). On approach to critical wetting at T = T(cW) the important coefficients w(jk) for k greater-than-or-equal-to 1 vanish rapidly with \T-T(cW)\; hence previous renormalization-group (RG) treatments of critical wetting remain essentially unchanged. However, these treatments neglect the variation of SIGMA(l) with l which, under RG flow, is seen here to destabilize wetting criticality; further analyses reported elsewhere, show that first-order transitions then arise in many cases.