Casimir force in the O(n -> infinity) model with free boundary conditions

Abstract

We present results for the temperature behavior of the Casimir force for a system with a film geometry with thickness $L$ subject to free boundary conditions and described by the $n\to \infty$ limit of the $O(n)$ model. These results extend over all temperatures, including the critical regime near the bulk critical temperature $T_c$, where the critical fluctuations determine the behavior of the force, and temperatures well below it, where its behavior is dictated by the Goldstone's modes contributions. The temperature behavior when the absolute temperature, $T$, is a finite distance below $T_c$, up to a logarithmic-in-$L$ proximity of the bulk critical temperature, is obtained both analytically and numerically; the critical behavior follows from numerics. The results resemble - but do not duplicate - the experimental curve behavior for the force obtained for ${}^4$He films.

16 pages, 3 figures, accepted for publication in Physical Review E. Abstract and author order changed to reflect the manuscript as rewritten, and comments changed to reflect the current status of the manuscript. Now published

References in corpus (29)

• Quantum magnetism and criticality
• Quantum Criticality
• 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
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• Thermodynamic Casimir effects involving interacting field theories with zero modes
• Aspect-ratio dependence of thermodynamic Casimir forces
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• Critical Casimir forces for Ising films with variable boundary fields
• Interplay of critical Casimir and dispersion forces
• Quantum Critical Paraelectrics and the Casimir Effect in Time
• Critical Casimir forces steered by patterned substrates
• Fluctuation-induced forces in periodic slabs: Breakdown of epsilon expansion at the bulk critical point and revised field theory
• Finite size behaviors of critical Ising model on a rectangle with free boundaries
• Casimir force induced by imperfect Bose gas
• Critical Casimir torques and forces acting on needles in two spatial dimensions
• Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces
• The imperfect Bose gas in d dimensions: critical behavior and Casimir forces
• Casimir force in O(n) lattice models with a diffuse interface
• Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$
• Scaling of solvation force in 2D Ising strip
• Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions
• Crossover from Goldstone to critical fluctuations: Casimir forces in confined O$(\mathbf{n})$ symmetric systems
• Casimir force in the rotor model with twisted boundary conditions
• Quantum critical scaling and the Gross-Neveu model in 2+1 dimensions

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