Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions

Abstract

In a recent study [Phys. Rev. E \textbf{94}, 022103 (2016)] it has been shown that, for a fluid film subject to critical adsorption, the resulting critical Casimir force (CCF) may significantly depend on the thermodynamic ensemble. Here, we extend that study by considering fluid films within the so-called ordinary surface universality class. We focus on mean-field theory, within which the OP profile satisfies Dirichlet boundary conditions and produces a nontrivial CCF in the presence of external bulk fields or, respectively, a nonzero total order parameter within the film. Our analytical results are supported by Monte Carlo simulations of the three-dimensional Ising model. We show that, in the canonical ensemble, i.e., when fixing the so-called total mass within the film, the CCF is typically repulsive instead of attractive as in the grand canonical ensemble. Based on the Landau-Ginzburg free energy, we furthermore obtain analytic expressions for the order parameter profiles and analyze the relation between the total mass in the film and the external bulk field.

arXiv comment22 pages, 15 figures. Version 2: minor corrections; added Journal reference

References in corpus (37)

• Critical Phenomena and Renormalization-Group Theory
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• The Theory of Boundary Critical Phenomena
• Critical Casimir effect in classical binary liquid mixtures
• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Monte Carlo simulation results for critical Casimir forces
• Tunability of Critical Casimir Interactions by Boundary Conditions
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
• Nonuniversal finite-size scaling in anisotropic systems
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• Critical dynamics in thin films
• Critical Casimir effect for colloids close to chemically patterned substrates
• Crossover of Critical Casimir forces between different surface universality classes
• Critical Casimir forces for Ising films with variable boundary fields
• Interplay of critical Casimir and dispersion forces
• Normal and lateral critical Casimir forces between colloids and patterned substrates
• The critical Binder cumulant in a two--dimensional anisotropic Ising model with competing interaction
• Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results
• Critical Casimir forces steered by patterned substrates
• Diversity of critical behavior within a universality class
• Crossing the coexistence line at constant magnetization
• Correlation Function in Ising Models
• Universality of the thermodynamic Casimir effect
• Forces between chemically structured substrates mediated by critical fluids
• Large-$n$ approach to thermodynamic Casimir effects in slabs with free surfaces
• Critical Casimir Forces for Films with Bulk Ordering Fields
• Critical adsorption and critical Casimir forces in the canonical ensemble
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Finite-Size Correlation Length and Violations of Finite-Size Scaling
• Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$
• Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble
• Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions
• Three-dimensional Ising model in the fixed-magnetization ensemble: a Monte Carlo study
• Finite-size effects in film geometry with nonperiodic boundary conditions: Gaussian model and renormalization-group theory at fixed dimension
• 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
• Pronounced minimum of the thermodynamic Casimir forces of O($\mathbf{n}$) symmetric film systems: Analytic theory

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