Finite-size scaling Casimir force function: Exact spherical-model results

Danchev, Daniel M

doi:10.1103/physreve.53.2104

Cited by 41 publications

(99 citation statements)

References 11 publications

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“…(4.49) remains valid for x < 0. It follows that 55) which is again consistent with the results of [24] and [25]. The scaling function Θ P ∞,3 (x) is plotted in Fig.…”

Section: Scaling Functions For Periodic Boundary Conditionssupporting

confidence: 77%

“…in agreement with [24], [25], and [52]. The residual grand potential ϕ P ∞,res,d can be computed along similar lines.…”

Section: Scaling Functions For Periodic Boundary Conditionssupporting

confidence: 49%

“…This prompted them to conclude that the universality class of the critical behavior at the condensation transition of the imperfect Bose gas is represented by the spherical model. On the other hand, they found that at d = 3 the Casimir amplitude ∆ C associated with the residual free energy at the critical point takes twice the value of its analog for the spherical model [24,25].…”

Section: Introductionmentioning

confidence: 99%

“…Using a coherent-state functional-integral formulation, we show that the leading asymptotic behavior near its bulk condensation transition is described by the n = ∞ analogs Θ P ∞,d of the above scaling functions Θ P d of the classical O(2n) real-valued φ 4 theory. This means, in particular, that for d = 3 the critical behavior of the imperfect Bose gas with PBCs is described by twice the exactly known scaling function of the mean spherical model [24,25].…”

Section: Introductionmentioning

confidence: 99%

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Fluctuation-induced forces in confined ideal and imperfect Bose gases

Diehl

Rutkevich

2017

Phys. Rev. E

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Fluctuation-induced ("Casimir") forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to d-dimensional films of size ∞ d−1 × D under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions, are determined for the ideal gas case with these BCs, where λ th and ξ are the thermal de-Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functionsξ ) describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free O(2) theory for BC = P, A, DD, DN, NN. For d = 3, they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions Υ BC d (x λ , x ξ , c1D, c2D) and Θ R d (x ξ , c1D, c2D) under the RBCs (∂z − c1)φ|z=0 = (∂z + c2)φ|z=D = 0 with c1 ≥ 0 and c2 ≥ 0 are also determined. The corresponding scaling functions Υ P ∞,d (x λ , x ξ ) and Θ P ∞,d (x ξ ) for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with n internal degrees of freedom in the limit n → ∞. Hence, for d = 3, Θ P ∞,d (x ξ ) is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit n → ∞ of this interacting Bose gas. Numerically and analytically exact results for the scaling function Θ DD ∞,3 (x ξ ) therefore follow from those of the O(2n) φ 4 model for n → ∞.

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“…(4.49) remains valid for x < 0. It follows that 55) which is again consistent with the results of [24] and [25]. The scaling function Θ P ∞,3 (x) is plotted in Fig.…”

Section: Scaling Functions For Periodic Boundary Conditionssupporting

confidence: 77%

“…in agreement with [24], [25], and [52]. The residual grand potential ϕ P ∞,res,d can be computed along similar lines.…”

Section: Scaling Functions For Periodic Boundary Conditionssupporting

confidence: 49%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fluctuation-induced forces in confined ideal and imperfect Bose gases

Diehl

Rutkevich

2017

Phys. Rev. E

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“…[47] one has performed measurements of the Casimir force in thin wetting films of binary liquid mixture. One the theoretical side, the effect has been studied via exact calculations in the two-dimensional Ising model [48][49][50][51][52][53][54][55][56][57], the three dimensional spherical model [58][59][60][61][62][63][64][65][66], via conformal-theoretical methods [67][68][69][70][71][72][73], within mean-field type calculations on Ising type [74][75][76][77][78] and XY models [80], through renormalization-group studies via ε-expansion [81][82][83][84][85][86][87][88] and via fixed dimension d techniques [87][88][89] of O(n) models, as well as via MonteCarlo calculations [79,[90][91]…”

Section: Introductionmentioning

confidence: 99%

Critical and near-critical phase behavior and interplay between the thermodynamic Casimir and van der Waals forces in a confined nonpolar fluid medium with competing surface and substrate potentials

Valchev

Dantchev

2015

Phys. Rev. E

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We study, using general scaling arguments and mean-field type calculations, the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance L from each other, confining some fluctuating fluid medium, say a non-polar one-component fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials ensuring the so-called (+, +) boundary conditions. The slabs, on the other hand, influence the fluid by long-range competing dispersion potentials, which represent irrelevant interactions in renormalization group sense. Under such conditions one usually expects attractive Casimir force governed by universal scaling function, pertinent to the extraordinary surface universality class of Ising type systems, to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given threshold thickness of the system L crit for a suitable set of slabs-fluid and fluid-fluid coupling parameters the competition between the effects due to the coatings and the slabs can result in sign change of the Casimir force acting between the surfaces confining the fluid when one changes the temperature T , the chemical potential of the fluid µ, or L. The last implies that by choosing specific materials for the slabs, coatings and the fluid for L L crit one can realize repulsive Casimir force with non-universal behavior which, upon increasing L, gradually turns into an attractive one described by an universal scaling function, depending only on the relevant scaling fields related to the temperature and the excess chemical potential, for L L crit . We presented arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force. It can be of interest, e.g., for designing nano-devices and for governing behavior of objects, say colloidal particles, at small distances. We have formulated the corresponding criterion for determination of L crit . The universality is regained for L L crit . We have also shown that for systems with L L crit the capillary condensation phase diagram suffers modifications which one does not observe in systems with purely short-ranged interactions.

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Casimir amplitudes in a quantum spherical model with long-range interaction

2000

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A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and "temporal size" 1/T ( T -temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions 1 2 σ < d < 3 2 σ , where 0 < σ ≤ 2 is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if d = σ, the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is ∆ = −16ζ(3)/[5σ(4π) σ/2 Γ (σ/2)]. The last implies that the universal constantc = 4/5 of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such thatc = 1. This is a generalization to the case of long-range interaction of the well known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for d = σ = 1 isc = 0.606.PACS. 05.70.Jk Critical Phenomena -64.60.i General studies of phase transitions

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Finite-size scaling Casimir force function: Exact spherical-model results

Cited by 41 publications

References 11 publications

Fluctuation-induced forces in confined ideal and imperfect Bose gases

Fluctuation-induced forces in confined ideal and imperfect Bose gases

Critical and near-critical phase behavior and interplay between the thermodynamic Casimir and van der Waals forces in a confined nonpolar fluid medium with competing surface and substrate potentials

Casimir amplitudes in a quantum spherical model with long-range interaction

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