Pronounced minimum of the thermodynamic Casimir forces of O(n) symmetric film systems: analytic theory.

Abstract

Thermodynamic Casimir forces of film systems in the O(n) universality classes with Dirichlet boundary conditions are studied below bulk criticality. Substantial progress is achieved in resolving the long-standing problem of describing analytically the pronounced minimum of the scaling function observed experimentally in ^{4}He films (n=2) by Garcia and Chan [Phys. Rev. Lett. 83, 1187 (1999)] and in Monte Carlo simulations for the three-dimensional Ising model (n=1) by O. Vasilyev etal. [Europhys. Lett. 80, 60009 (2007)]. Our finite-size renormalization-group approach describes the film systems as the limit of finite-slab systems with vanishing aspect ratio. This yields excellent agreement with the depth and the position of the minimum for n=1 and semiquantitative agreement with the minimum for n=2. Our theory also predicts a pronounced minimum for the n=3 Heisenberg universality class.