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Upton, P. J.; Borjan, Z.

doi:10.1103/physrevb.88.155418

Cited by 11 publications

(13 citation statements)

References 35 publications

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“…(105a) and (110a) pertaining to linear MFT can be compared with the generally expected behavior within the Ising universality class in the grand canonical ensemble for B = 0 and H 1 = ∞. In this case, local-functional approaches [72,128], exact results for the Ising strip [129], and estimates based on the transfer-matrix method [130] indicate that Ξ (gc)…”

Section: B Mean Field Theorymentioning

confidence: 95%

“…For the present purposes, however, we have to compare bulk pressures which emerge by coupling the bulk either canonically or grand canonically to a film of a given total mass Φ. In the case of a grand canonical coupling, the corresponding bulk pressure p (gc) b is a function of the chemical potential µ = μ(Φ) required to satisfy the constraint of fixed mass Φ in the film [125]. In contrast, in the case of a canonical coupling, the pressure p (c) b is not a function of μ, but it is determined from the condition that the mean mass densities ϕ in the film and in the bulk must be the same.…”

Section: B Mean Field Theorymentioning

confidence: 99%

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Critical adsorption and critical Casimir forces in the canonical ensemble

et al. 2016

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Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean field theory (MFT) based on a Ginzburg-Landau free energy functional as well as via Monte Carlo simulations of the threedimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a non-integrable divergence of the mean field order parameter (OP) profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.

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Section: B Mean Field Theorymentioning

confidence: 95%

Section: B Mean Field Theorymentioning

confidence: 99%

Critical adsorption and critical Casimir forces in the canonical ensemble

et al. 2016

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“…Also for the two-dimensional Ising model with various boundary conditions exact results were obtained [47][48][49][50][51][52]. In the case of the three-dimensional Ising universality class and strongly symmetry breaking boundary conditions, quite accurate results had been obtained by using the extended de Gennes-Fisher local-functional method [53][54][55]. O(n)-symmetric systems with periodic boundary conditions had been studied using a functional renormalization group approach [56].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic Casimir effect in films: The exchange cluster algorithm

Hasenbusch

2015

Phys. Rev. E

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We study the thermodynamic Casimir force for films with various types of boundary conditions and the bulk universality class of the three-dimensional Ising model. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. In particular, we employ the exchange or geometric cluster cluster algorithm [Heringa and Blöte, Phys. Rev. E 57, 4976 (1998)]. In a previous work, we demonstrated that this algorithm allows us to compute the thermodynamic Casimir force for the plate-sphere geometry efficiently. It turns out that also for the film geometry a substantial reduction of the statistical error can achieved. Concerning physics, we focus on (O,O) boundary conditions, where O denotes the ordinary surface transition. These are implemented by free boundary conditions on both sides of the film. Films with such boundary conditions undergo a phase transition in the universality class of the two-dimensional Ising model. We determine the inverse transition temperature for a large range of thicknesses L(0) of the film and study the scaling of this temperature with L(0). In the neighborhood of the transition, the thermodynamic Casimir force is affected by finite size effects, where finite size refers to a finite transversal extension L of the film. We demonstrate that these finite size effects can be computed by using the universal finite size scaling function of the free energy of the two-dimensional Ising model.

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“…Along the symmetry line (h = 0), more precise estimates of the universal Casimir scaling functions for the 3D Ising universality class and film geometry have been obtained via MC simulations of the Ising model [47][48][49]. Few theoretical approaches were devised to address this problem: in addition to the mean field results [50], its is worthwhile mentioning the extended de Gennes-Fisher local functional method [51,52] and a long wavelength analysis of density functional theory [10,53]. The latter investigations have been also extended away from the symmetry line (h = 0) providing predictions on the shape of the critical Casimir scaling function in the off-critical case [53][54][55].…”

Section: A Force Profilesmentioning

confidence: 99%

Solvent-mediated forces in critical fluids

Anzini

Parola

2016

Phys. Rev. E

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The effective interaction between two planar walls immersed in a fluid is investigated by use of Density Functional Theory in the super-critical region of the phase diagram. A hard core Yukawa model of fluid is studied with special attention to the critical region. To achieve this goal a new formulation of the Weighted Density Approximation coupled with the Hierarchical Reference Theory, able to deal with critical long wavelength fluctuations, is put forward and compared with other approaches. The effective interaction between the walls is seen to change character on lowering the temperature: The strong oscillations induced by layering of the molecules, typical of the depletion mechanism in hard core systems, are gradually smoothed and, close to the critical point, a long range attractive tail emerges leading to a scaling form which agrees with the expectations based on the critical Casimir effect. Strong corrections to scaling are seen to affect the results up to very small reduced temperatures. By use of Derjaguin approximation, this investigation has natural implications for the aggregation of colloidal particles in critical solvents.

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Off-critical Casimir effect in Ising slabs with antisymmetric boundary conditions ind=3

Cited by 11 publications

References 35 publications

Critical adsorption and critical Casimir forces in the canonical ensemble

Critical adsorption and critical Casimir forces in the canonical ensemble

Thermodynamic Casimir effect in films: The exchange cluster algorithm

Solvent-mediated forces in critical fluids

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