Pronounced minimum of the thermodynamic Casimir forces of O($\mathbf{n}$) 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 R. Garcia and M.H.W. 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., EPL $80,60009(2007)$. Our finite-size renormalization-group approach 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.

1 figure

References in corpus (12)

• The Casimir effect: from quantum to critical fluctuations
• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Critical Casimir force in ${}^4$He films: confirmation of finite-size scaling
• Monte Carlo simulation results for critical Casimir forces
• Critical Casimir Effect in superfluid wetting films
• Thinning of superfluid films below the critical point
• Aspect-ratio dependence of thermodynamic Casimir forces
• Diversity of critical behavior within a universality class
• Large-$n$ approach to thermodynamic Casimir effects in slabs with free surfaces
• Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces
• Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$
• Crossover from Goldstone to critical fluctuations: Casimir forces in confined O$(\mathbf{n})$ symmetric systems

Cited by in corpus (10)

• Critical Casimir Effect: Exact Results
• Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions
• Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Crossover from low-temperature to high-temperature fluctuations. II. Nonuniversal thermodynamic Casimir forces of anisotropic systems
• Crossover from low-temperature to high-temperature fluctuations. I. Thermodynamic Casimir forces of isotropic systems
• Inverse scattering-theory approach to the exact large-$n$ solutions of $O(n)$ ${\varphi }^4$ models on films and semi-infinite systems bounded by free surfaces
• Fluctuation induced forces in critical films with disorder at their surfaces
• Exact solution for the order parameter profiles and the Casimir force in ${}^4$He superfluid films in an effective field theory
• Casimir effect for a Bose-Einstein condensate inside a cylindrical tube