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

TL;DR

This paper provides an exact numerical analysis of thermodynamic Casimir forces in a three-dimensional interacting model with free surfaces, capturing key experimental and simulation features across all temperatures.

Contribution

It introduces an exact solution for the classical O(n) phi^4 model in 3D film geometry, using a self-consistent Schrödinger equation approach, applicable to both partially and fully discretized models.

Findings

Exact scaled Casimir force results at all temperatures.

Reproduction of qualitative features observed in experiments and simulations.

Identification of a pronounced force minimum below the critical point.

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 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.