Crossover from Goldstone to critical fluctuations: Casimir forces in confined O$(\mathbf{n})$ symmetric systems

Abstract

We study the crossover between thermodynamic Casimir forces arising from long-range fluctuations due to Goldstone modes and those arising from critical fluctuations. Both types of forces exist in the low-temperature phase of O$(n)$ symmetric systems for $n>1$ in a $d$-dimensional $L_{\parallel }^{d-1}\times L$ slab geometry with a finite aspect ratio $\rho =L/L_{\parallel }$. Our finite-size renormalization-group treatment for periodic boundary conditions describes the entire crossover from the Goldstone regime with a nonvanishing constant tail of the finite-size scaling function far below $T_c$ up to the region far above $T_c$ including the critical regime with a minimum of the scaling function slightly below $T_c$. Our analytic result for $\rho \ll 1$ agrees well with Monte Carlo data for the three-dimensional XY model. A quantitative prediction is given for the crossover of systems in the Heisenberg universality class.

2 figures

References in corpus (7)

• 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
• Thinning of superfluid films below the critical point
• Thermodynamic Casimir effects involving interacting field theories with zero modes
• Aspect-ratio dependence of thermodynamic Casimir forces
• Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$

Cited by in corpus (6)

• Critical Casimir Effect: Exact Results
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Exact Critical Casimir Amplitude of Anisotropic Systems from Conformal Field Theory and Self-Similarity of Finite-Size Scaling Functions in $d\ge 2$ Dimensions
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Repulsive to Attractive Fluctuation-Induced Forces in Disordered Landau-Ginzburg Model
• Exact solution for the order parameter profiles and the Casimir force in ${}^4$He superfluid films in an effective field theory