Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$

Abstract

We present a field-theoretic study of the critical Casimir force of the Ising universality class in a $d$-dimensional $L_{\parallel }^{d-1}\times L$ slab geometry with a finite aspect ratio $\rho =L/L_{\parallel }$ above, at, and below $T_c$. The result of a perturbation approach at fixed dimension $d=3$ is presented that describes the dependence on the aspect ratio in the range $\rho \gtrsim 1/4$. Our analytic result for the Casimir force scaling function for $\rho =1/4$ agrees well with recent Monte Carlo data for the three-dimensional Ising model in slab geometry with periodic boundary conditions above, at, and below $T_c$.

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References in corpus (19)

• Critical Casimir force in ${}^4$He films: confirmation of finite-size scaling
• Monte Carlo simulation results for critical Casimir forces
• Fluctuation - induced forces in critical fluids
• The Thermodynamic Casimir Effect in ${}^4$He Films near $T_{\lambda }$: Monte Carlo Results
• Critical Binder cumulant in two-dimensional anisotropic Ising models
• The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results
• Nonuniversal finite-size scaling in anisotropic systems
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• Thinning of superfluid films below the critical point
• Thermodynamic Casimir effects involving interacting field theories with zero modes
• Casimir forces, surface fluctuations, and thinning of superfluid films
• Interplay of critical Casimir and dispersion forces
• Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results
• Fluctuation-induced forces in periodic slabs: Breakdown of epsilon expansion at the bulk critical point and revised field theory
• Diversity of critical behavior within a universality class
• Universality of the thermodynamic Casimir effect
• Casimir force in O(n) lattice models with a diffuse interface
• Non-universal size dependence of the free energy of confined systems near criticality
• Non-universal critical Casimir force in confined ${}^4$He near the superfluid transition

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• Finite-size effects in film geometry with nonperiodic boundary conditions: Gaussian model and renormalization-group theory at fixed dimension
• Crossover from Goldstone to critical fluctuations: Casimir forces in confined O$(\mathbf{n})$ symmetric systems
• Critical free energy and Casimir forces in rectangular geometries
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Critical Casimir forces from the equation of state of quantum critical systems
• 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
• Anisotropic scaling of the two-dimensional Ising model I: the torus
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