Scaling of the Specific Heat of Confined Helium near<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

Chen, Tar-Pin; Gasparini, Francis M.

doi:10.1103/physrevlett.40.331

Cited by 89 publications

(52 citation statements)

References 15 publications

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“…The function f depends on the boundary conditions and the geometry of the system. Liquid helium 4 He has been a very good ground both for testing nite-size scaling theory and measuring the critical exponents that go along with a second order phase transition in the case of a complex order parameter. Measurements of the super uid density 3] and speci c heat 4] on helium lms, however, fail to verify the nite-size scaling theory.…”

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confidence: 99%

“…5{7] and those data. Furthermore, new experiments on liquid 4 He under microgravity conditions are planned 11] to examine the nite{size scaling properties of the speci c heat. The above mentioned eld theoretical calculations are based on methods such as a loop expansion which systematically includes corrections due to uctuations around a mean-eld solution.…”

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confidence: 99%

“…In this paper we study the e ect of Dirichlet boundary conditions on the nite{size scaling behavior of the speci c heat of 4 He in a lm geometry L L H with L H. These boundary conditions are believed to simulate the boundary conditions of the real helium lms more accurately 6,7]. With these boundary conditions, the super uid order parameter vanishes in the top and the bottom of the lm.…”

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confidence: 99%

“…We use the x y model to describe the uctuations of the order parameter in super uid 4 He near the {critical point (cf. e.g.…”

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confidence: 99%

“…where V m is the molar volume of 4 He at saturated vapor pressure at T . The unit of length a (i.e., the lattice spacing a in the x y model) can be determined in such a way that the x y model describes the uctuations of the order parameter in liquid helium.…”

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Scaling of the Specific Heat in Superfluid Films

Schultka

Manousakis

1995

Phys. Rev. Lett.

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We study the speci c heat of the x y model on lattices L L H with L H (i.e. on lattices representing a lm geometry) using the Cluster Monte{Carlo method. In the H {direction we apply Dirichlet boundary conditions so that the order parameter in the top and bottom layers is zero. We nd that our results for the speci c heat of various thickness size H collapse on the same universal scaling function. The extracted scaling function of the speci c heat is in good agreement with the experimentally determined universal scaling function using no free parameters. 64.60.Fr, 67.40.Kh The theory of second order phase transitions is based on the assumption that at temperatures close to the critical temperature T c there is only one dominating length scale associated with the critical behavior of the system, the correlation length. Because the correlation length diverges as the critical temperature is approached the microscopic details of the system become irrelevant for the exponents describing the most singular dependence of the thermodynamic functions on the reduced temperature t = T=T c 1. This intuitive picture has its foundation in the renormalization group treatment of second order phase transitions. Within the renormalization group treatment it becomes evident that the critical behavior can be divided into di erent universality classes which are characterized by a set of critical exponents.If the system is con ned in a nite geometry (e.g. a cubic or lm geometry) the nite{size scaling theory 1] is thought to describe well the behavior of the system at temperatures near T c . The intuitive idea behind the nite{size scaling theory is that nite{size e ects are observed when the bulk correlation length becomes of the order of the nite system size, i.e. for our case here the lm thickness H. For a physical quantity O this statement can be expressed as follows 2]:The dimensionless ratio on the left-hand-side of the above equation is a universal function f(x) of the dimensionless ratio x = H= , i.e. in our present work the lm thickness measured with respect to the correlation length. The function f depends on the boundary conditions and the geometry of the system. Liquid helium 4 He has been a very good ground both for testing nite-size scaling theory and measuring the critical exponents that go along with a second order phase transition in the case of a complex order parameter. Measurements of the super uid density 3] and speci c heat 4] on helium lms, however, fail to verify the nite-size scaling theory. Field theoretical calculations for the standard Landau{Ginzburg free energy functional in di erent geometries with Dirichlet boundary conditions have been carried out 5{8]. New speci c heat measurements 9] and also a reanalysis 10] of the old speci c heat data 4] show good agreement between the results of the calculations reported in Refs. 5{7] and those data. Furthermore, new experiments on liquid 4 He under microgravity conditions are planned 11] to examine the nite{size scaling properties of the speci c heat. The above ...

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confidence: 99%

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confidence: 99%

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confidence: 99%

“…We use the x y model to describe the uctuations of the order parameter in super uid 4 He near the {critical point (cf. e.g.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Scaling of the Specific Heat in Superfluid Films

Schultka

Manousakis

1995

Phys. Rev. Lett.

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Scaling of Confined 4He at the Superfluid Transition

Gasparini

Rhee

1991

Excitations in Two-Dimensional and Three-Dimensional Quantum Fluids

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Critical behavior of the free surface of liquid 4He near the λ point

Wong

1979

J Low Temp Phys

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The noncriticality of the free surface of liquid 4He near the h point and the finite-size scaling postulate are combined to show that the surface tension can have two singularities, one due to rounding and another due to shifting. The rounding singularity can be reduced, via a further scaling assumption, to that previously suggested by Sobvanin and Hohenberg. Results from calculations based on continuous symmetry models and experiments on topologically 2D 4He films are used to argue that the shift singularity is Itl 1 =, which is consistent with the leading singularity observed by Magerlein and Sanders.

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Scaling of the Specific Heat of Confined Helium nearTλ

Cited by 89 publications

References 15 publications

Scaling of the Specific Heat in Superfluid Films

Scaling of the Specific Heat in Superfluid Films

Scaling of Confined 4He at the Superfluid Transition

Critical behavior of the free surface of liquid 4He near the λ point

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