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Influence of the Casimir effect on the binding potential for three-dimensional wetting

Alessio Squarcini*

José M. Romero-Enrique

Andrew O. Parry

  • Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, 30 Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg

  • Departamento de Física Atómica, Molecular y Nuclear, Área de Física Teórica, Universidad de Sevilla, Avenida de Reina Mercedes s/n, 41012 Seville, Spain and Instituto Carlos I de Física Teórica y Computacional, Campus Universitario Fuentenueva, Calle Dr. Severo Ochoa, 18071 Granada, Spain

  • *Contact author: alessio.squarcini@uni.lu
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Phys. Rev. E 113, 024133 – Published 24 February, 2026

DOI: https://doi.org/10.1103/5gx7-spg3

Abstract

We provide comprehensive details of how a previously overlooked entropic, or low-temperature Casimir contribution, WC, 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 WMF. We determine the functional dependence of WC 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 WC 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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Phys. Rev. E 113, 024133– Published 24 February, 2026
  • Received 15 September 2025
  • Accepted 20 January 2026
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