Theory of Critical Phenomena in Finite-Size Systems

Brankov, J.G.; Danchev, Daniel M; Tonchev, N. S.

doi:10.1142/4146

Cited by 221 publications

(277 citation statements)

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“…Experimentally, critical Casimir forces have been first measured indirectly by studying the thickness of thin wetting films upon passing thermodynamically a critical end point in the phase diagram of the fluid [13,14]. For classical binary liquid mixtures [15,16] as well as for quantum binary liquids 3 He / 4 He [17,18] and liquid 4 He [19,20] such experiments have provided evidence of the critical Casimir effect in agreement with theoretical results obtained via Monte Carlo (MC) simulations [21][22][23][24][25][26].…”

Section: Introductionsupporting

confidence: 55%

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Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

et al. 2014

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Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basis of the Derjaguin approximation. The range of validity of the latter is assessed via mean-field theory. This assessment shows that the Derjaguin approximation is reliable in experimentally relevant regimes, so that we extend it to Janus particles endowed with opposing adsorption preferences. Our analysis indicates that critical Casimir interactions are capable of achieving well-defined, reversible alignments both of chemically homogeneous and of Janus cylinders.

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Section: Introductionsupporting

confidence: 55%

“…Since its prediction [2], the critical Casimir effect has attracted numerous theoretical investigations (see, e.g., Refs. [3] and [4] and references therein) revealing both an intriguing instance of solvent-mediated effective interactions and a classical analogue of the celebrated Casimir effect in quantum electrodynamics [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

et al. 2014

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“…General reviews of FSS can be found in Refs. [53][54][55]; a summary of FSS theory which focuses on symmetry-breaking boundary conditions is found in Ref. [40], while FSS at a quantum phase transition is discussed in Ref.…”

Section: A General Propertiesmentioning

confidence: 99%

“…In the FSS limit, the singular part of the free energy density obeys the scaling ansatz [53][54][55][56] …”

Section: A General Propertiesmentioning

confidence: 99%

Critical behavior in the presence of an order-parameter pinning field

2017

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We apply a recently advocated simulation scheme that employs a local order-parameter pinning field to study quantum critical phenomena in the two-dimensional square-lattice bilayer quantum Heisenberg model. Using a world-line quantum Monte Carlo approach, we show that for this model, the pinning-field approach allows to locate the quantum critical point over a wide range of pinning-field strengths. However, the identification of the quantum critical scaling behavior is found to be hard since the pinning field introduces strong corrections to scaling. In order to further elucidate the scaling behavior in this situation, we also study an improved classical lattice model in the three-dimensional Ising universality class by means of Monte Carlo simulations on large lattice sizes, which allow us to employ refined finite-size scaling considerations. A renormalization group analysis exhibits the presence of an important crossover effect from the zero pinning-field to a critical adsorption fixed point. In line with field-theoretical results, we find that at the critical adsorption fixed point the shortdistance expansion of the order-parameter profile exhibits a new universal critical exponent. This result also implies the presence of slowly decaying scaling corrections, which we analyze in detail.

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“…The perfect Bose-gas is the simplest quantum mechanical system showing the spontaneous breaking of a continuous symmetry (Bose-Einstein condensation) for which the Casimir effect should appear. To our knowledge, this has surprisingly not been studied before.We first recall the definition of the Casimir amplitude at critical points or for phases with broken symmetry [2] [3]. Let…”

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confidence: 99%

The Casimir effect for the Bose-gas in slabs

Martin¹,

Zagrebnov²

2006

Europhys. Lett.

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Abstract. -We study the Casimir effect for the perfect Bose-gase in the slab geometry for various boundary conditions. We show that the grand canonical potential per unit area at the bulk critical chemical potential µ = 0 has the standard asymptotic form with universal Casimir terms.In contrast to the well-known Casimir effect for the photon gas, see e.g.[1], this effect for the massive quantum particles (quantum gases) is much less explored. In the present letter we consider the case of the perfect Bose-gas. The perfect Bose-gas is the simplest quantum mechanical system showing the spontaneous breaking of a continuous symmetry (Bose-Einstein condensation) for which the Casimir effect should appear. To our knowledge, this has surprisingly not been studied before.We first recall the definition of the Casimir amplitude at critical points or for phases with broken symmetry [2] [3]. Let

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Theory of Critical Phenomena in Finite-Size Systems

Cited by 221 publications

References 0 publications

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

Critical behavior in the presence of an order-parameter pinning field

The Casimir effect for the Bose-gas in slabs

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