Curvature contributions to the capillary-wave Hamiltonian for a pinned interface

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Abstract
The curvature contributions to the capillary-wave Hamiltonian of a pinned interface are analyzed with the mean-field version of the Landau-Ginzburg-Wilson theory supplemented by the crossing constraint. The resulting fourth-order Hamiltonian can be unambiguously written in the Helfrich form with the coefficients depending on the local distance l of the fluctuating interface from the flat substrate. The expressions for these coefficients are derived and their l dependence is discussed; they all consist of exponentially decaying terms multiplied by polynomials. The expression for the l-dependent stiffness coefficient present in the fourth-order Hamiltonian differs from one derived recently within a second-order theory. © 1996 The American Physical Society.