A possible explanation of sound conversion at the free surface of superfluid helium near T<sub>λ</sub>

Xiong, G. M.; Gong, Chang‐De

doi:10.1088/0953-8984/1/44/037

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Besides changing the local static critical behaviour surfaces have also an effect on the dynamic critical behaviour [122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138]. A central aspect of the works on dynamic surface critical behaviour concerns the possible classification of the distinct surface dynamic universality classes, similar to what has been done in the past for the dynamical bulk critical behaviour [139].…”

Section: Critical Dynamics At Surfacesmentioning

confidence: 93%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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Abstract. In the past perfect surfaces have been shown to yield a local critical behaviour that differs from the bulk critical behaviour. On the other hand surface defects, whether they are of natural origin or created artificially, are known to modify local quantities. It is therefore important to clarify whether these defects are relevant or irrelevant for the surface critical behaviour.The purpose of this review is two-fold. In the first part we summarise some of the important results on surface criticality at perfect surfaces. Special attention is thereby paid to new developments as for example the study of surface critical behaviour in systems with competing interactions or of surface critical dynamics. In the second part the effect of surface defects (presence of edges, steps, quenched randomness, lines of adatoms, regular geometric patterns) on local critical behaviour in semi-infinite systems and in thin films is discussed in detail. Whereas most of the defects commonly encountered are shown to be irrelevant, some notable exceptions are highlighted. It is shown furthermore that under certain circumstances non-universal local critical behaviour may be observed at surfaces.

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Section: Critical Dynamics At Surfacesmentioning

confidence: 93%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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“…26 There exist also a number of papers dealing with finite-size effects on dynamic critical behavior and dynamic surface critical behavior. [18][19][20]22,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] In other works, finite-size systems with long-range interactions or quenched disorder were investigated. [44][45][46] Recently, Gambassi and Dietrich 47 presented a fairly detailed study of the familiar model A (Refs.…”

Section: Introductionmentioning

confidence: 99%

Dynamic critical behavior of modelAin films: Zero-mode boundary conditions and expansion near four dimensions

Diehl

Chamati

2009

Phys. Rev. B

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The critical dynamics of relaxational stochastic models with nonconserved n-component order parameter and no coupling to other slow variables ͑"model A"͒ is investigated in film geometries for the cases of periodic and free boundary conditions. The Hamiltonian H governing the stationary equilibrium distribution is taken to be O͑n͒ symmetric and to involve, in the case of free boundary conditions, the boundary terms ͐ B j c j 2 / 2 associated with the two confining surface planes B j , j =1,2, at z = 0 and z = L. Both enhancement variables c j are presumed to be subcritical or critical, so that no long-range surface order can occur above the bulk critical temperature T c,ϱ . A field-theoretic renormalization-group study of the dynamic critical behavior at d =4−⑀ bulk dimensions is presented, with special attention paid to the cases where the classical theories involve zero modes at T c,ϱ . This applies when either both c j take the critical value c sp associated with the special surface transition or else periodic boundary conditions are imposed. Owing to the zero modes, the ⑀ expansion becomes ill-defined at T c,ϱ . Analogously to the static case, the field theory can be reorganized to obtain a well-defined small-⑀ expansion involving half-integer powers of ⑀, modulated by powers of ln ⑀. This is achieved through the construction of an effective ͑d −1͒-dimensional action for the zero-mode component of the order parameter by integrating out its orthogonal component via renormalization-group improved perturbation theory. Explicit results for the scaling functions of temperature-dependent finite-size susceptibilities at temperatures T Ն T c,ϱ and of layer and surface susceptibilities at the bulk critical point are given to orders ⑀ and ⑀ 3/2 , respectively. They show that L dependent shifts of the multicritical special point occur along the temperature and enhancement axes. For the case of periodic boundary conditions, the consistency of the expansions to O͑⑀ 3/2 ͒ with exact large-n results is shown. We also discuss briefly the effects of weak anisotropy, relating theories whose Hamiltonian involves a generalized square gradient term B kl ‫ץ‬ k · ‫ץ‬ l to those with a conventional ٌ͑͒ 2 term.

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Critical thermal boundary resistance of4He above and belowT ?: Renormalization-group theory

Frank

Dohm

1991

Z. Physik B - Condensed Matter

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A possible explanation of sound conversion at the free surface of superfluid helium near T_λ

Cited by 6 publications

References 14 publications

Critical phenomena at perfect and non-perfect surfaces

Critical phenomena at perfect and non-perfect surfaces

Dynamic critical behavior of modelAin films: Zero-mode boundary conditions and expansion near four dimensions

Critical thermal boundary resistance of4He above and belowT ?: Renormalization-group theory

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A possible explanation of sound conversion at the free surface of superfluid helium near Tλ

Cited by 6 publications

References 14 publications

Critical phenomena at perfect and non-perfect surfaces

Critical phenomena at perfect and non-perfect surfaces

Dynamic critical behavior of modelAin films: Zero-mode boundary conditions and expansion near four dimensions

Critical thermal boundary resistance of4He above and belowT ?: Renormalization-group theory

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A possible explanation of sound conversion at the free surface of superfluid helium near T_λ