Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces

Abstract

The limit n to infinity of the classical O(n) phi^4 model on a 3d film with free surfaces is studied. Its exact solution involves a self-consistent 1d Schrödinger equation, which is solved numerically for a partially discretized as well as for a fully discrete lattice model. Numerically exact results are obtained for the scaled Casimir force at all temperatures. Obtained via a single framework, they exhibit all relevant qualitative features of the thermodynamic Casimir force known from wetting experiments on Helium-4 and Monte Carlo simulations, including a pronounced minimum below the bulk critical point.

5 pages, 2 figures

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• Direct simulation of critical Casimir forces
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
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• Anisotropic scaling of the two-dimensional Ising model I: the torus
• Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface
• The O(n) ${\varphi }^4$ model with free surfaces in the large-$n$ limit: Some exact results for boundary critical behaviour, fluctuation-induced forces and distant-wall corrections
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Pronounced minimum of the thermodynamic Casimir forces of O($\mathbf{n}$) symmetric film systems: Analytic theory
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Comment on "Casimir force in the $O(n\to \infty )$ model with free boundary conditions"
• Inverse scattering-theory approach to the exact large-$n$ solutions of $O(n)$ ${\varphi }^4$ models on films and semi-infinite systems bounded by free surfaces
• Inverse scattering theory and trace formulae for one-dimensional Schrödinger problems with singular potentials
• Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry
• Reply to Comment on "Casimir force in the $O(n\to \infty )$ model with free boundary conditions"
• The three-dimensional $O(n)$ ${\varphi }^4$ model on a strip with free boundary conditions: exact results for a nontrivial dimensional crossover in the limit $n\to \infty$