Pronounced minimum of the thermodynamic Casimir forces of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:math>symmetric film systems: Analytic theory

Dohm, V.

doi:10.1103/physreve.90.030101

Cited by 12 publications

(27 citation statements)

References 43 publications

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“…The value of the scaling function of the Casimir force at the minimum is not reported in Ref. [18], but from the presented plot, see Fig. 1(b), it can be evaluated to be about X Cas,min,RG −1.8, which is very close to our finding within Ap1 with M = 0.…”

Section: Discussion and Concluding Remarkssupporting

confidence: 89%

“…This is, of Figure 6: A comparison of the experimental data of the Casimir force, the scattered curves, reported in [2] with the prediction of the Ψ theory when M = 0 and M = 0.2, the solid curves. The prediction of the Renormalization Group theory [18] is also presented -the red curve with the inverted triangles marks. The green dashed vertical line at −3.91 marks the Monte Carlo prediction for the occurrence of Kosterlitz-Thouless transition in the film [15].…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…The first attempt in that direction was made in [3,4], where the authors studied within the ε expansion the behavior of the force in 4 He above T λ . Recent progress below T λ has been made in [18]; see the red curve marked with inverted triangles in Fig. 6.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

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Exact solution for the order parameter profiles and the Casimir force in 4He superfluid films in an effective field theory

Dantchev

Rudnick

Vassilev

et al. 2019

Physica A: Statistical Mechanics and its Applications

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We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburg's Ψ-theory for the behavior of the Casimir force in a film of 4 He in equilibrium with its vapor near the superfluid transition point. We consider three versions of the theory, depending on the way one determines its parameters from the experimental measurements. We present exact results for the behavior of the order parameter profiles and of the Casimir force within this theory, which is characterized by d = 3, ν = 2/3 and β = 1/3, where d is the bulk spatial dimension and ν and β are the usual critical exponents. In addition, we revisit relevant experiments [1] and [2] in terms of our findings. We find reasonably good agreement between our theoretical predictions and the experimental data. We demonstrate analytically that our calculated force is attractive. The position of the extremum is predicted to be at x min = π, with x = (L/ξ 0 )(T/T λ − 1) 1/ν , which value effectively coincides with the experimental finding x min = 3.2 ± 0.18. Here L is the thickness of the film, T λ is the bulk critical temperature and ξ 0 is the correlation length amplitude of the system for temperature T > T λ . The theoretically predicted position of the minimum does not depend on the one adjustable parameter, M, entering the theory. The situation is different with respect to the largest absolute value of the scaling function, which depends on both ξ 0 and on M. For this value the experiments yield −1.30. If one uses ξ 0 = 1.63 Å, as in the original Ψ theory of Ginsburg, one obtains the closest approach to the experimental value −1.848 with M = 0. If one uses M = 0.5, as inferred from other experiments, along with the best currently accepted experimental value for ξ 0 , ξ 0 = 1.432 Å, then the maximum value of the force is predicted to be −1.58. The effective theory considered here is not consistent with critical point universality; furthermore it incorrectly predicts ordering in the film in violation of known rigorous results. These issues are discussed in the text. vasilvas@imbm.bas.bg and padjon@imbm.bas.bg (and Peter A Djondjorov)

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Section: Discussion and Concluding Remarkssupporting

confidence: 89%

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

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Exact solution for the order parameter profiles and the Casimir force in 4He superfluid films in an effective field theory

Dantchev

Rudnick

Vassilev

et al. 2019

Physica A: Statistical Mechanics and its Applications

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“…denotes the scaled reduced temperature (relative to the bulk critical point) of the film critical point. MC simulations of the Ising model [43] yield a value x f c −7.6 for the film critical point, while field theoretic renormalization group studies [44] predict x f c −6.44. Here and in the following, when considering the regime t < 0, i.e., x < 0, we define x as…”

Section: A Exact Analysis For B = 0 and Location Of The Film Criticamentioning

confidence: 99%

“…(15)] arising within MFT. This deficiency can be overcome by including fluctuation effects within a renormalization group approach [44].…”

Section: Computationmentioning

confidence: 99%

Ensemble dependence of critical Casimir forces in films with Dirichlet boundary conditions

et al. 2019

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In a recent study [Phys. Rev. E 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 order parameter (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. Additionally, we study the influence of fluctuations by means of 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 repulsive for large absolute values of the total OP, 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.is defined in terms of the bulk OP φ b , which, near criticality, behaves asfor µ = 0 and t → 0, (6a) φ b,µ = sgn(µ)φ (0) µ |µ| 1/δ , for t = 0 and µ → 0, (6b) in the case of a vanishing external field µ and a vanishing reduced temperature t, respectively.

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Critical Casimir effect: Exact results

Dantchev

Dietrich

2023

Physics Reports

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Pronounced minimum of the thermodynamic Casimir forces ofO(n)symmetric film systems: Analytic theory

Cited by 12 publications

References 43 publications

Exact solution for the order parameter profiles and the Casimir force in 4He superfluid films in an effective field theory

Exact solution for the order parameter profiles and the Casimir force in 4He superfluid films in an effective field theory

Ensemble dependence of critical Casimir forces in films with Dirichlet boundary conditions

Critical Casimir effect: Exact results

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