Exact thermodynamic Casimir forces for an interacting three-dimensional   model system in film geometry with free surfaces
  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 Schr\"odinger 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. 
H. W. Diehl, Daniel Gr\"uneberg, Martin Hasenbusch, Alfred Hucht,   Sergei B. Rutkevich, Felix M. Schmidt
cond-mat.stat-mech cond-mat.soft hep-th