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Previous treatments of three-dimensional (3D) short-ranged wettingtransitions have missed an entropic or low temperature Casimir contribution tothe binding potential describing the interaction between the unbindinginterface and wall. This we determine by exactly deriving the interfacial modelfor 3D wetting from a more microscopic Landau-Ginzburg-Wilson Hamiltonian. TheCasimir term changes the interpretation of fluctuation effects occurring atwetting transitions so that, for example, mean-field predictions are no longerobtained when interfacial fluctuations are ignored. While the Casimircontribution does not alter the surface phase diagram, it significantlyincreases the adsorption near a first-order wetting transition and changescompletely the predicted critical singularities of tricritical wetting,including the non-universality occurring in 3D arising from interfacialfluctuations. Using the numerical renormalization group we show that, forcritical wetting, the asymptotic regime is extremely narrow with the growth ofthe parallel correlation length characterised by an effective exponent inquantitative agreement with Ising model simulations, resolving a longstandingcontroversy.

Casimir contribution to the interfacial Hamiltonian for 3D wetting