Monte Carlo simulation results for critical Casimir forces

Abstract

The confinement of critical fluctuations in soft media induces critical Casimir forces acting on the confining surfaces. The temperature and geometry dependences of such forces are characterized by universal scaling functions. A novel approach is presented to determine them for films via Monte Carlo simulations of lattice models. The method is based on an integration scheme of free energy differences. Our results for the Ising and the XY universality class compare favourably with corresponding experimental results for wetting layers of classical binary liquid mixtures and of 4He, respectively.

14 pages, 5 figures

References in corpus (13)

• Critical Phenomena and Renormalization-Group Theory
• The `Friction' of Vacuum, and other Fluctuation-Induced Forces
• Casimir forces in binary liquid mixtures
• Critical Casimir force in ${}^4$He films: confirmation of finite-size scaling
• Critical Behaviour of the 3D XY-Model: A Monte Carlo Study
• Fluctuation - induced forces in critical fluids
• The Thermodynamic Casimir Effect in ${}^4$He Films near $T_{\lambda }$: Monte Carlo Results
• The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results
• Critical Casimir Effect in superfluid wetting films
• Thinning of superfluid films below the critical point
• Casimir forces, surface fluctuations, and thinning of superfluid films
• Fluctuation-induced forces in periodic slabs: Breakdown of epsilon expansion at the bulk critical point and revised field theory
• Correlation Function in Ising Models

Cited by in corpus (90)

• Critical Casimir effect in classical binary liquid mixtures
• The Casimir effect: from quantum to critical fluctuations
• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Critical Casimir forces in colloidal suspensions on chemically patterned surfaces
• Tunability of Critical Casimir Interactions by Boundary Conditions
• Collective behavior of colloids due to critical Casimir interactions
• Nonadditivity of 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 for films in the 3D Ising universality class: Symmetry breaking boundary conditions
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• Critical Casimir effect for colloids close to chemically patterned substrates
• Crossover of Critical Casimir forces between different surface universality classes
• Thermodynamic Casimir effects involving interacting field theories with zero modes
• Aspect-ratio dependence of thermodynamic Casimir forces
• Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: Renormalized local functional theory
• 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
• Off-critical Casimir effect in Ising Slabs with Symmetric Boundary Conditions in d=3
• Normal and lateral critical Casimir forces between colloids and patterned substrates
• Trapping colloids near chemical stripes via critical Casimir forces
• Critical Casimir interaction of ellipsoidal colloids with a planar wall
• Critical Casimir Effect: Exact Results
• Critical Casimir forces steered by patterned substrates
• Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate
• Diversity of critical behavior within a universality class
• The specific heat, the energy density and the thermodynamic Casimir force in the neighbourhood of the lambda-transition
• The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
• Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions
• The thermodynamic Casimir effect in the neighbourhood of the lambda-transition: A Monte Carlo study of an improved three dimensional lattice model
• Many-body effects for critical Casimir forces
• Large-$n$ approach to thermodynamic Casimir effects in slabs with free surfaces
• Critical adsorption and critical Casimir forces for geometrically structured confinements
• Casimir force induced by imperfect Bose gas
• Critical Casimir torques and forces acting on needles in two spatial dimensions
• Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques
• Critical Casimir Forces for Films with Bulk Ordering Fields
• Critical adsorption and critical Casimir forces in the canonical ensemble
• Critical Casimir forces between homogeneous and chemically striped surfaces
• Fluctuation-induced forces in strongly anisotropic critical systems
• Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces
• Critical Casimir Interactions Between Spherical Particles in the Presence of the Bulk Ordering Fields
• Structure and aggregation of colloids immersed in critical solvents
• Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions
• Casimir force in O(n) lattice models with a diffuse interface
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Yet another method to compute the thermodynamic Casimir force in lattice models
• Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$
• Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions
• Casimir force in the O(n -> infinity) model with free boundary conditions
• Dimensional crossovers and Casimir forces for the Bose gas in anisotropic optical lattices
• Finite-size effects in film geometry with nonperiodic boundary conditions: Gaussian model and renormalization-group theory at fixed dimension
• Critical free energy and Casimir forces in rectangular geometries
• The square lattice Ising model on the rectangle II: Finite-size scaling limit
• Critical Casimir force in the presence of random local adsorption preference
• Casimir effect in swimmer suspensions
• Kosterlitz-Thouless transition in thin films: A Monte Carlo study of three-dimensional lattice models
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Direct simulation of critical Casimir forces
• Critical Casimir amplitudes for $n$-component ${\varphi }^4$ models with O(n)-symmetry breaking quadratic boundary terms
• Tuning effective interactions close to the critical point in colloidal suspensions
• Critical Casimir forces in the presence of random surface fields
• Properties of the solvation force of a two-dimensional Ising strip in scaling regimes
• Casimir force in the rotor model with twisted boundary conditions
• Critical Casimir forces between defects in the 2D Ising model
• Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface
• Bulk and boundary effects on the decay of the thermodynamic Casimir force
• Pronounced minimum of the thermodynamic Casimir forces of O($\mathbf{n}$) symmetric film systems: Analytic theory
• Critical Casimir force in the superfluid phase: effect of fluctuations
• 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
• The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation
• Critical Casimir forces in a magnetic system: An experimental protocol
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions
• Casimir interaction of rod-like particles in a two-dimensional critical system
• Solvent mediated forces in critical fluids
• Fluctuation induced forces in critical films with disorder at their surfaces
• Critical Casimir forces between planar and crenellated surfaces
• Exact solution for the order parameter profiles and the Casimir force in ${}^4$He superfluid films in an effective field theory
• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
• Magnetization profiles at the upper critical dimension as solutions of the integer Yamabe problem
• Casimir forces for the ideal Bose gas in anisotropic optical lattices: the effect of alternating sign upon varying dimensionality
• Critical Casimir Interactions and Percolation: the quantitative description of critical fluctuations
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Reversing the Critical Casimir force by shape deformation
• Critical $1$- and $2$-point spin correlations for the $O(2)$ model in $3d$ bounded domains
• Tricritical Casimir forces and order parameter profiles in wetting films of ${}^3\text{He}$ -${}^4\text{He}$ mixtures
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations
• Proposed fitting function for the critical Casimir force on ${}^4$He film below the $\lambda$ point
• 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 $n\to \infty$