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

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 4He 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 et al. [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.