The Kosterlitz–Thouless transition in thin films: a Monte Carlo study of three-dimensional lattice models

Hasenbusch, Martin

doi:10.1088/1742-5468/2009/02/p02005

Cited by 22 publications

(71 citation statements)

References 63 publications

(294 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For Goldstone modes such as spin waves in the XY model the free energy difference arises because standing waves form in the direction perpendicular to the film surface, eliminating modes that can still propagate in the bulk. This gives K G = V k B T ζ(3)/(8πd 3 ), a result well confirmed in computer simulations [7,12,17,18] and analytic calculations [19] for XY spin waves. The experiments in helium did find a difference in film thickness between low temperatures and above T λ similar to but larger than this prediction [9,11]; however a later theory [16] showed that this was primarily due to energy differences in the waves at the free surface of the film and bulk, resulting in a thinning magnitude nearly double the the expression for K G above.We doubt very much that second sound propagates at all in saturated helium films.…”

supporting

confidence: 77%

Non-universal Casimir effect in saturated superfluid⁴He films at T_λ

Abraham

Williams

Penanen

2014

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Measurements of Casimir effects in 4 He films in the vicinity of the bulk superfluid transition temperature T λ have been carried out, where changes in the film thickness and the superfluid density are both monitored as a function of temperature. The Kosterlitz-Thouless superfluid onset temperature in the film is found to occur just as the Casimir dip in the film thickness from critical fluctuations becomes evident. Additionally, a new film-thickening effect is observed precisely at T λ when the temperature is swept extremely slowly. We propose that this is a non-universal Casimir effect arising from the viscous suppression of second sound modes in the film. PACS numbers: 67.25.dj, 67.25.bh, 67.25.dg, 68.35.Md Copyright 2013. All rights reserved.Saturated liquid 4 He films, in contact with the bulk liquid, form an illuminating model system as a condensed matter analogue of the electromagnetic Casimir effect. Thermal fluctuations in the film are limited by the finite thickness of the film, leading to a free-energy difference with the unlimited fluctuations in the bulk [1]. This causes a change in the film thickness as the atoms move to minimize the free energy. The equilibrium thickness is determined by an energy-balance relation per atom of mass m for a film of thickness d at a height h above the bulk helium surface,where the substrate van der Waals interaction U vdW at the film surface [2], including retardation effects, is given byThis is the main term determining the film thickness, with γ 0 the van der Waals constant equal to 3.59×10 −13 ergÅ 3 for a Cu substrate, and d 1/2 = 193Å . The fluctuation-induced Casimir forces K then produce small additional shifts ∆d as the temperature is swept near the bulk superfluid transition temperature T λ . The force K crit comes from critical fluctuations near the transition temperature, i.e. the vortex loops in the model of Ref. [3]. Finite-size scaling theories [4][5][6] 43Å the amplitude of the coherence length above T λ (using the normalization of Ref.[7]), and V = 45.8Å 3 the volume per helium atom. Experiments [8][9][10][11] have observed a dip in the film thickness corresponding to these critical fluctuations in agreement with simulations [12], and data collapse of films of different thickness confirmed the form of the scaling. One factor not well determined in experiments to date is the location of the Kosterlitz-Thouless (KT) superfluid transition relative to the dip in film thickness. A quartz microbalance oscillator technique at 5 MHz [10] seemed to show the transition as occurring at a temperature somewhat below the bottom of the dip, but the exact location could not be pinpointed because the high frequency greatly broadens the KT transition [13].The term K G in Eq. 1 refers to the free energy difference between bulk and film due to thermally excited Goldstone modes [14]. It was originally proposed that such modes should include the second sound mode in the case of liquid helium [11,15,16], but since we question this we include instead a separate term K 2 fo...

show abstract

supporting

confidence: 77%

Non-universal Casimir effect in saturated superfluid⁴He films at T_λ

Abraham

Williams

Penanen

2014

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…However we note that this straightforward approach is subject to systematic errors which get suppressed only logarithmically with increasing L. This makes the accuracy of the numerical or experimental determination of the critical parameters quite problematic. This problem can be overcome by the so-called matching method [56,73,81,86,87,89,90], which allows us to control the whole pattern of the logarithmic corrections, leaving only power-law corrections.…”

Section: B Finite-size Behavior At the Bkt Transitionmentioning

confidence: 99%

Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

Delfino

Vicari

2017

Phys. Rev. A

View full text Add to dashboard Cite

We investigate systems of interacting bosonic particles confined within slab-like boxes of size L 2 ×Z with Z ≪ L, at their three-dimensional (3D) BEC transition temperature Tc, and below Tc where they experience a quasi-2D Berezinskii-Kosterlitz-Thouless transition (at TBKT < Tc depending on the thickness Z). The low-temperature phase below TBKT shows quasi-long-range order: the planar correlations decay algebraically as predicted by the 2D spin-wave theory. This dimensional crossover, from a 3D behavior for T Tc to a quasi-2D critical behavior for T TBKT, can be described by a transverse finite-size scaling limit in slab geometries. We also extend the discussion to the offequilibrium behavior arising from slow time variations of the temperature across the BEC transition. Numerical evidence of the 3D→2D dimensional crossover is presented for the Bose-Hubbard model defined in anisotropic L 2 × Z lattices with Z ≪ L.

show abstract

“…Since long-range order is rigorously ruled out for finite thickness L at all temperatures T > 0 by the Mermin-Wagner theorem [14,16]; only a rounded L < ∞ transition is possible when T > 0, where the O(2) case is special in that a Kosterlitz-Thouless transition to a low-temperature phase with quasi-long-range order is known to occur at a nonzero temperature T KT (L) < T c (see [38] and its references). The destruction of long-range order at low temperatures caused by low-energy fluctuations is a nonperturbative phenomenon ("nonperturbative mass generation").…”

Section: Introductionmentioning

confidence: 99%

Large-napproach to thermodynamic Casimir effects in slabs with free surfaces

et al. 2014

Self Cite

View full text Add to dashboard Cite

The classical n-vector ϕ{4} model with O(n) symmetrical Hamiltonian H is considered in a ∞{2}×L slab geometry bounded by a pair of parallel free surface planes at separation L. Standard quadratic boundary terms implying Robin boundary conditions are included in H. The temperature-dependent scaling functions of the excess free energy and the thermodynamic Casimir force are computed in the large-n limit for temperatures T at, above, and below the bulk critical temperature T_{c}. Their n=∞ limits can be expressed exactly in terms of the spectrum and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. This equation is solved by numerical means for two distinct discretized versions of the model: in the first ("model A"), only the coordinate z across the slab is discretized and the integrations over momenta conjugate to the lateral coordinates are regularized dimensionally; in the second ("model B"), a simple cubic lattice with periodic boundary conditions along the lateral directions is used. Renormalization-group ideas are invoked to show that, in addition to corrections to scaling ∝L{-1}, anomalous ones ∝L{-1}lnL should occur. They can be considerably decreased by taking an appropriate g→∞ (T_{c}→∞) limit of the ϕ{4} interaction constant g. Depending on the model A or B, they can be absorbed completely or to a large extent in an effective thickness L_{eff}=L+δL. Excellent data collapses and consistent high-precision results for both models are obtained. The approach to the low-temperature Goldstone values of the scaling functions is shown to involve logarithmic anomalies. The scaling functions exhibit all qualitative features seen in experiments on the thinning of wetting layers of {4}He and Monte Carlo simulations of XY models, including a pronounced minimum of the Casimir force below T_{c}. The results are in conformity with various analytically known exact properties of the scaling functions.

show abstract

The Kosterlitz–Thouless transition in thin films: a Monte Carlo study of three-dimensional lattice models

Cited by 22 publications

References 63 publications

Non-universal Casimir effect in saturated superfluid⁴He films at T_λ

Non-universal Casimir effect in saturated superfluid⁴He films at T_λ

Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

Large-napproach to thermodynamic Casimir effects in slabs with free surfaces

Contact Info

Product

Resources

About

The Kosterlitz–Thouless transition in thin films: a Monte Carlo study of three-dimensional lattice models

Cited by 22 publications

References 63 publications

Non-universal Casimir effect in saturated superfluid4He films at Tλ

Non-universal Casimir effect in saturated superfluid4He films at Tλ

Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

Large-napproach to thermodynamic Casimir effects in slabs with free surfaces

Contact Info

Product

Resources

About

Non-universal Casimir effect in saturated superfluid⁴He films at T_λ

Non-universal Casimir effect in saturated superfluid⁴He films at T_λ