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.

arXiv comment16 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 (46)

• Quantum magnetism and criticality
• Quantum Criticality: competing ground states in low dimensions
• Quantum Criticality
• The Casimir effect: from quantum to critical fluctuations
• The Mechanical Response of Vacuum
• Casimir forces in binary liquid mixtures
• 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
• Fluctuation - induced forces in critical fluids
• The Thermodynamic Casimir Effect in ${}^4$He Films near $T_{\lambda }$: Monte Carlo Results
• Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance
• The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results
• Quantum description of spherical spins
• 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
• Casimir interactions in Ising strips with boundary fields: exact results
• Critical dynamics in thin films
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• Aspect-ratio dependence of thermodynamic Casimir forces
• Casimir forces, surface fluctuations, and thinning of superfluid films
• Thermodynamic Casimir effects involving interacting field theories with zero modes
• Critical Casimir forces for Ising films with variable boundary fields
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• Interplay of critical Casimir and dispersion forces
• Quantum Critical Paraelectrics and the Casimir Effect in Time
• Critical Casimir forces steered by patterned substrates
• 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
• The specific heat, the energy density and the thermodynamic Casimir force in the neighbourhood of the lambda-transition
• Finite size behaviors of critical Ising model on a rectangle with free boundaries
• Exact Three Dimensional Casimir Force Amplitude, $C$-function and Binder's Cumulant Ratio: Spherical Model Results
• 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 $T_c$
• Yet another method to compute the thermodynamic Casimir force in lattice models
• 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
• Critical Casimir forces for $\mathcal{O}(n)$ systems with long-range interaction in the spherical limit
• Properties of the solvation force of a two-dimensional Ising strip in scaling regimes
• Casimir force in the rotor model with twisted boundary conditions
• Quantum critical scaling and the Gross-Neveu model in 2+1 dimensions

Cited by in corpus (17)

• Critical Casimir Effect: Exact Results
• Large-$n$ approach to thermodynamic Casimir effects in slabs with free surfaces
• Fluctuation-induced forces in confined ideal and imperfect Bose gases
• Spin ice thin films: Large-N theory and Monte Carlo simulations
• 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
• Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface
• Pronounced minimum of the thermodynamic Casimir forces of O($\mathbf{n}$) symmetric film systems: Analytic theory
• 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
• Comment on "Casimir force in the $O(n\to \infty )$ model with free boundary conditions"
• Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class
• 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
• Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry
• Reply to Comment on "Casimir force in the $O(n\to \infty )$ model with free boundary conditions"
• The three-dimensional $O(n)$ ${\varphi }^4$ model on a strip with free boundary conditions: exact results for a nontrivial dimensional crossover in the limit $n\to \infty$
• From Laplacian-to-Adjacency Matrix for Continuous Spins on Graphs