Effective potentials, constraints, and critical wetting theory

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Abstract
Renormalization-group theory based on an effective wall-interface potential W(l;T,h), h being the external field, predicts nonuniversality for three-dimensional critical wetting with short-range forces; but Monte Carlo simulations disagree seriously. To illuminate this, general derivations of W(l) are reported: perturbative analysis using a zero-crossing constraint on a mean-field profile to fix the interface location, l, reveals defects in previous results. However, leading renormalization-group predictions remain unchanged. A novel integral constraint for defining l is solved exactly and yields the same conclusion.