2014/01/31 by V. Dohm · 11 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Boundary value problem #Casimir effect #Combinatorics #Condensed matter physics #Dirichlet boundary condition #Geometry #Ising model #Material Dynamics and Properties #Mathematical physics #Mathematics #Monte Carlo method #Phase Equilibria and Thermodynamics #Physics #Quantum mechanics #Renormalization group #Scaling #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamic limit #Thermodynamics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.90.030101
published in Physical Review E 90(3), 030101 (American Physical Society) · 1 figure
openalex publication_date 2014/09/25 · arxiv created 2014/09/28 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.