Renormalization-group theory of critical phenomena near the Lambda transition of4He

Dohm, V.

doi:10.1007/bf00681623

Cited by 58 publications

(15 citation statements)

References 59 publications

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“…In the evaluation of (20) leading to (24) we dismissed a constant term stemming from the constant in (21), the higher-order terms (~ No ~/3 or No 1) because they come from p.o. in more than one direction, and a term ~ n~ because it is noncritical (that means eventually negligible near the transition point).…”

Section: Eo(vn) = (Fih]f) = ~ Dsrge(r)go(r)mentioning

confidence: 99%

A model for the λ-transition of helium

Fließbach

1991

Il Nuovo Cimento D

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Summary. --Guided by the analogy to the Bose-Einstein condensation of the ideal Bose gas (IBG) we propose a new model for the ~-transition of liquid helium. Deviating from the IBG our model uses phase-ordered and localized single-particle functions. This means that finite groups of particles are assumed to be phase-locked. These phase correlations can be related to the singularity at the transition point and to the occurrence of the superfluid density. The model leads to the following results: 1) a possible explanation of the logarithmic singularity of the specific heat, 2) a characteristic functional form for the superfluid density which yields excellent fits to the experimental data, 3) a quantitative prediction of a small nonzero entropy content of the superfluid component.PACS 67.20 -Quantum effects on the structure and dynamics of nondegenerate fluids (e.g., normal phase liquid helium 4).

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Section: Eo(vn) = (Fih]f) = ~ Dsrge(r)go(r)mentioning

confidence: 99%

A model for the λ-transition of helium

Fließbach

1991

Il Nuovo Cimento D

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“…Vacuum diagrams up to five-loop order determining the Helmholtz free energy Γ 0 for M 0 = 0, r 0 > 0. Diagrams(6),(10) and(11) do not contribute to A(u, ǫ). The pole terms derived from the vacuum diagrams are given in (A1)-(A54) of App.…”

mentioning

confidence: 99%

Five-loop additive renormalization in theφ4theory and amplitude functions of the minimally renormalized specific heat in three dimensions

et al. 1998

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We present an analytic five-loop calculation for the additive renormalization constant A(u, ǫ) and the associated renormalization-group function B(u) of the specific heat of the O(n) symmetric φ 4 theory within the minimal subtraction scheme. We show that this calculation does not require new fiveloop integrations but can be performed on the basis of the previous five-loop calculation of the four-point vertex function combined with an appropriate identification of symmetry factors of vacuum diagrams. We also determine the amplitude function F + (u) of the specific heat in three dimensions for n = 1, 2, 3 above T c and F − (u) for n = 1 below T c up to five-loop order, without using the ǫ = 4 − d expansion. Accurate results are obtained from Borel resummations of B(u) for n = 1, 2, 3 and of the amplitude functions for n = 1. Previous conjectures regarding the smallness of the resummed higherorder contributions are confirmed. Combining our results for B(u) and F + (u) for n = 1, 2, 3 with those of a recent three-loop calculation of F − (u) for general n in d = 3 dimensions we calculate Borel resummed universal amplitude

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“…(71). Further Goldstone singularities are contained in the two-loop diagrams (5), (12), (17), (18), (19) and (22) in Fig. 4.…”

Section: A Correlation Lengthsmentioning

confidence: 96%

“…We have omitted diagrams with tadpole insertions since their sum, being equal to δ φ ′ 0 (x) , vanishes according to Eq. (19). Eq.…”

Section: Bare Free Energymentioning

confidence: 99%

Minimal renormalization without ϵ-expansion: Amplitude functions for O(n) symmetric systems in three dimensions below Tc

Burnett¹,

Stroesser²,

Dohm

1997

Nuclear Physics B

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Massive field theory at fixed dimension d < 4 is combined with the minimal subtraction scheme to calculate the amplitude functions of thermodynamic quantities for the O(n) symmetric φ 4 model below T c in two-loop order. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities are shown to cancel among themselves leaving a finite result in the limit of zero external field. From the free energy we calculate the amplitude functions in zero field for the order parameter, specific heat and helicity modulus (superfluid density) in three dimensions. We also calculate the q 2 part of the inverse of the wavenumber-dependent transverse susceptibility χ T (q) which provides an independent check of our result for the helicity modulus. The two-loop contributions to the superfluid density and specific heat below T c turn out to be comparable in magnitude to the one-loop contributions, indicating the necessity of higher-order calculations and Padé-Borel type resummations.

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Renormalization-group theory of critical phenomena near the Lambda transition of4He

Cited by 58 publications

References 59 publications

A model for the λ-transition of helium

A model for the λ-transition of helium

Five-loop additive renormalization in theφ4theory and amplitude functions of the minimally renormalized specific heat in three dimensions

Minimal renormalization without ϵ-expansion: Amplitude functions for O(n) symmetric systems in three dimensions below Tc

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