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Casimir Contribution to the Interfacial Hamiltonian for 3D Wetting
Alessio Squarcini1, José M Romero-Enrique2, Andrew O Parry3
1Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, D-70569 Stuttgart, Germany; IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany; and Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020, Innsbruck, Austria.
Abstract:
Previous treatments of three-dimensional (3D) short-ranged wetting transitions have missed an entropic or low-temperature Casimir contribution to the binding potential describing the interaction between the unbinding interface and wall. This we determine by exactly deriving the interfacial model for 3D wetting from a more microscopic Landau-Ginzburg-Wilson Hamiltonian. The Casimir term changes the interpretation of fluctuation effects occurring at wetting transitions so that, for example, mean-field predictions are no longer obtained when interfacial fluctuations are ignored. While the Casimir contribution does not alter the surface phase diagram, it significantly increases the adsorption near a first-order wetting transition and changes completely the predicted critical singularities of tricritical wetting, including the nonuniversality occurring in 3D arising from interfacial fluctuations. Using the numerical renormalization group, we show that, for critical wetting, the asymptotic regime is extremely narrow with the growth of the parallel correlation length characterized by an effective exponent in quantitative agreement with Ising model simulations, resolving a long-standing controversy.
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