Critical exponents predicted by grouping of Feynman diagrams in 4 model

Kaupužs, J.

doi:10.1002/1521-3889(200104)10:4<299::aid-andp299>3.3.co;2-a

Cited by 7 publications

(44 citation statements)

References 28 publications

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“…In particular, it is believed that accurate experimental measurements of specific heat C p of liquid helium very close to the λ-transition point in zero gravity conditions (in space) [1] provide a convincing evidence of overall correctness of the perturbative RG approach. The aim of our paper is to show that this conclusion is not unambiguous, since these experimental data as well as those of the superfluid fraction of liquid helium can be equally well or even better interpreted by a completely different set of critical exponents provided by our recently developed theory [2].…”

Section: Introductionsupporting

confidence: 89%

“…Alternatively, we have fit the data within a moving window t ∈ [t i ; 100t i ] of the reduced temperatures to the simplest possible ansatz [1], whereas the dashed curve shows schematically a behaviour expected from [2].…”

Section: Interpretation Of the Specific Heat Datamentioning

confidence: 91%

“…with fixed exponents α = −1/13 and ∆ = 5/13 proposed in [2,6]. It is consistent with the idea that specific heat can have a logarithmic correction, as discussed in [2].…”

Section: Interpretation Of the Specific Heat Datamentioning

confidence: 99%

“…It is consistent with the idea that specific heat can have a logarithmic correction, as discussed in [2]. The power-like singularity is recovered at A = 0.…”

Section: Interpretation Of the Specific Heat Datamentioning

confidence: 99%

“…Note that only the possibility and not the necessity of the logarithmic correction follows from the theory [2]. However, the presence of the logarithmic correction for specific heat, perhaps, is a quite general feature: the logarithmic singularity (as a special case of the logarithmic correction when α = 0) of specific heat is a rigorously stated fact in 2D Ising model [8], and our Monte Carlo simulation data for 3D Ising model [6] also supports the logarithmic singularity.…”

Section: Interpretation Of the Specific Heat Datamentioning

confidence: 99%

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Interpretation of experimental data near λ-transition point in liquid helium

Kaupužs

2005

Eur. Phys. J. B

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The recently published experimental data for specific heat C p of liquid helium in zero gravity conditions very close to the λ-transition have been discussed. We have shown that these data allow different interpretations. They can be well interpreted within the perturbative RG approach and within our recently developed theory, as well. Allowing the logarithmic correction, the corresponding fits lie almost on top of each other over the whole range of the reduced temperatures t (for bin averaged data) 6.3 · 10 −10 < t < 8.8 · 10 −3 . However, the plot of the effective exponent α eff (t) suggests that the behaviour of C p , probably, changes very close to T λ . To clarify this question, we need more accurate data for t < 10 −7 . In addition, we show that the experimental data for superfluid fraction of liquid helium close to T λ within t ∈ [3 · 10 −7 ; 10 −4 ] can be better fit by our exponents ν = 9/13 ≃ 0.6923, ∆ = 5/13 ≃ 0.3846 than by the RG exponents ν ≃ 0.6705 and ∆ ≃ 0.5. The latter ones are preferable to fit the whole measured range t ∈ [3 · 10 −7 ; 10 −2 ] where, however, remarkable systematic deviations appear. Our estimated value 0.694 ± 0.017 of the asymptotic exponent ν well agrees with the theoretical prediction ν = 9/13.

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Section: Introductionsupporting

confidence: 89%

Section: Interpretation Of the Specific Heat Datamentioning

confidence: 91%

“…with fixed exponents α = −1/13 and ∆ = 5/13 proposed in [2,6]. It is consistent with the idea that specific heat can have a logarithmic correction, as discussed in [2].…”

Section: Interpretation Of the Specific Heat Datamentioning

confidence: 99%

“…It is consistent with the idea that specific heat can have a logarithmic correction, as discussed in [2]. The power-like singularity is recovered at A = 0.…”

Section: Interpretation Of the Specific Heat Datamentioning

confidence: 99%

Section: Interpretation Of the Specific Heat Datamentioning

confidence: 99%

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Interpretation of experimental data near λ-transition point in liquid helium

Kaupužs

2005

Eur. Phys. J. B

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Polarization kinetics in ferroelectrics with regard to fluctuations

Kaupužs¹,

Rimshans²,

Smyth³

2008

Modelling Simul. Mater. Sci. Eng.

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Polarization in ferroelectrics, described by the Landau-Ginzburg Hamiltonian, is considered, based on a multi-dimensional Fokker-Planck equation. This formulation describes the time evolution of the probability distribution function over the polarization field configurations in the presence of a time dependent external field. The Fokker-Planck equation in a Fourier representation is obtained, which can then be solved numerically for a finite number of modes. Calculation results are presented for one and three modes. These results show the hysteresis of the mean polarization as well as that of the mean squared gradient of the polarization.

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Universal amplitude ratios in the Ising model in three dimensions

Gordillo‐Guerrero¹,

Kenna²,

Ruiz‐Lorenzo³

2011

J. Stat. Mech.

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We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A + /A − in the three-dimensional Ising model via the impact angle φ of complex temperature zeros. We also measure the correlationlength critical exponent ν from finite-size scaling, and the specific-heat exponent α through hyperscaling. Extrapolations to the thermodynamic limit yield φ = 59.2(1.0) • , A + /A − = 0.56(3), ν = 0.63048(32) and α = 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.

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Critical exponents predicted by grouping of Feynman diagrams in 4 model

Cited by 7 publications

References 28 publications

Interpretation of experimental data near λ-transition point in liquid helium

Interpretation of experimental data near λ-transition point in liquid helium

Polarization kinetics in ferroelectrics with regard to fluctuations

Universal amplitude ratios in the Ising model in three dimensions

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