We provide comprehensive details of how a previously overlooked entropic, or low-temperature Casimir contribution, $W_C$, to the total binding potential for three-dimensional short-ranged wetting may be determined from a microscopic Landau-Ginzburg-Wilson Hamiltonian. The entropic contribution comes from the many microscopic configurations corresponding to a given interfacial one, which arise from bulklike fluctuations about the mean-field (MF) constrained profile, and adds to the usual MF contribution $W_{\text{MF}}$. We determine the functional dependence of $W_C$ on the interface (and wall) shape using a boundary integral method which can be cast as a diagrammatic expansion with each diagram corresponding to successively higher-order exponentially decaying contributions. The decay of $W_C$ is qualitatively different for first-order and critical wetting with the change in form occurring at the MF tricritical point. Including the Casimir contribution to the binding potential preserves the global surface phase diagram but changes, radically, predictions for fluctuation effects at first-order and tricritical wetting, even when capillary-wave fluctuations are not considered.

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• Classical statistical mechanics
• Interfaces
• Critical phenomena
• Path-integral methods