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Abstract
In order to satisfy exact sum-rule requirements for correlation function structure at complete wetting, a two-field Hamiltonian , modelling the coupling of order-parameter fluctuations near the wall and unbinding interface, has been introduced. The model is characterized by a stiffness matrix, , whose bare (unrenormalized) elements are related to the mean-field free energy. We extend previous renormalization group studies to include the position dependence of the matrix elements and derive an elegant operator relationship which shows that the flow of the cross-coupling term parallels that of the free energy. This establishes the validity of a stiffness matrix - free-energy relation in the presence of fluctuation effects at the marginal dimension d = 3 for systems with short-ranged forces. We further show that an analogous relation exists for systems with long-ranged molecular interactions.
Published Version
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