On the critical exponents for the λ transition in liquid helium

Pogorelov, A. A.; Suslov, I.

doi:10.1134/s0021364007130097

Cited by 21 publications

(40 citation statements)

References 15 publications

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“…We focus here on the Ising model N = 1 which exhibits a standard critical behavior in d = 2, and the corresponding critical exponents. Notice that the perturbative method that works well in d = 3 fails here: for instance, the fixed-dimension expansion that provides the best results in d = 3 yields, in d = 2 and at five loops, η = 0.145(14) [27] in contradiction with the exact value η = 1/4[? ].…”

Section: Results For the Critical Exponentsmentioning

confidence: 99%

Nonperturbative renormalization group preserving full-momentum dependence: Implementation and quantitative evaluation

Benitez

Blaizot²,

Chaté³

et al. 2012

Phys. Rev. E

105

128

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We present in detail the implementation of the Blaizot-Méndez-Wschebor (BMW) approximation scheme of the nonperturbative renormalization group, which allows for the computation of the full momentum dependence of correlation functions. We discuss its signification and its relation with other schemes, in particular the derivative expansion. Quantitative results are presented for the testground of scalar O(N ) theories. Besides critical exponents which are zero-momentum quantities, we compute in three dimensions in the whole momentum range the two-point function at criticality and, in the high temperature phase, the universal structure factor. In all cases, we find very good agreement with the best existing results.

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Section: Results For the Critical Exponentsmentioning

confidence: 99%

Nonperturbative renormalization group preserving full-momentum dependence: Implementation and quantitative evaluation

Benitez

Blaizot²,

Chaté³

et al. 2012

Phys. Rev. E

105

128

View full text Add to dashboard Cite

show abstract

“…[6], there arose a discrepancy between the Monte Carlo simulation and the microgravity-environment experiment; see also Ref. [23]. As a matter of fact, the microgravity experiment [22] reports a critical exponent α = −0.0127 (3).…”

Section: Summary and Discussionmentioning

confidence: 99%

Numerical diagonalization analysis of the criticality of the(2+1)-dimensionalXYmodel: Off-diagonal Novotny’s method

Nishiyama

2008

Phys. Rev. E

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The criticality of the (2 + 1)-dimensional XY model is investigated with the numerical diagonalization method. So far, it has been considered that the diagonalization method would not be very suitable for analyzing the criticality in large dimensions (d ≥ 3); in fact, the tractable system size with the diagonalization method is severely restricted. In this paper, we employ Novotny's method, which enables us to treat a variety of system sizes N = 6, 8, . . . , 20 (N : the number of spins constituting a cluster). For that purpose, we develop an off-diagonal version of Novotny's method to adopt the off-diagonal (quantum-mechanical XY ) interaction. Moreover, in order to improve the finite-size-scaling behavior, we tune the coupling-constant parameters to a scale-invariant point.As a result, we estimate the critical indices as ν = 0.675(20) and γ/ν = 1.97(10).

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“…Below the scale k c , i.e., in the IR scaling region it holds κ = 0, the anomalous dimension vanishes, and the field-independent wavefunction renormalization freezes out at its value Z kc reached at the lower end k c of the WF crossover region, while the couplings of the potential and the couplingȲ k show up tree-level scaling (see Eqs. (31), (32) and (33) forκ = 0). The reciprocal of the scale k c can be identified with the correlation length ξ = 1/k c .…”

Section: B Crossover Scalingmentioning

confidence: 99%

“…In Tables VIII and IX we listed the values of the anomalous dimension η and the correlation length's critical exponent ν for the d = 3 dimensional O(1) and O(N ≥ 2) models published in the recent years (without pretending to be complete), concentrating on the NLO and NNLO results of the GE. We also list the best available BMW results [20,21] and some results obtained by other methods [30][31][32][33][34][35][36][37] that can be considered the 'world's best' values, as well as experimental values for the Ising model [38]. Before turning to a discussion of Tables VIII and IX, it is worthwhile to emphasize that the results for the anomalous dimension are rather sensitive to the field-dependence of the wavefunction renormalization and that of the coupling of the O(∂ 4 ) term (see a detailed discussion in [5]).…”

Section: Asymptotics For Large Nmentioning

confidence: 99%

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in O(N) models

2018

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The effect of the O(∂ 4 ) terms of the gradient expansion on anomalous dimension η and the correlation length's critical exponent ν of the Wilson-Fisher fixed point has been determined for the Euclidean O(N ) model for N = 1 and the number of dimensions 2 < d < 4 as well as for N ≥ 2 and d = 3. Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory for N ≥ 2 is well approximated by the effective average action preserving O(N ) symmetry with the accuracy of O(η).

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On the critical exponents for the λ transition in liquid helium

Cited by 21 publications

References 15 publications

Nonperturbative renormalization group preserving full-momentum dependence: Implementation and quantitative evaluation

Nonperturbative renormalization group preserving full-momentum dependence: Implementation and quantitative evaluation

Numerical diagonalization analysis of the criticality of the(2+1)-dimensionalXYmodel: Off-diagonal Novotny’s method

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in O(N) models

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