Ising-Model Critical Indices in Three Dimensions from the Callan-Symanzik Equation

Baker, George A.; Nickel, B. G.; Green, Melville S.; Meiron, D. I.

doi:10.1103/physrevlett.36.1351

Cited by 295 publications

(247 citation statements)

References 15 publications

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“…It was also found that one (the smallest) of the eigenvalue exponents characterizing the evolution of this term under the renormalization group in a neighborhood of the Bose FP is proportional to the specific heat exponent α. Since α is believed to be negative at that point, and that is supported experimentally [17] and theoretically [18,19,20,21], the interaction is irrelevant. Consequently, the Bose FP should be stable in three dimensions.…”

Section: Introductionmentioning

confidence: 96%

Critical behavior of certain antiferromagnets with complicated ordering: Four-loopɛ-expansion analysis

Mudrov

Varnashev

2001

Phys. Rev. B

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The critical behavior of a complex N -component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in (4 − ε) dimensions. By using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced and resummed by the Borel-Leroy transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases N = 2 and N = 3 shows that the model has an anisotropic stable fixed point governing the continuous phase transitions with new critical exponents. This is supported by the estimate of the critical dimensionality N c = 1.445(20) obtained from six loops via the exact relation N c = 1 2 n c established for the complex and real hypercubic models.

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Section: Introductionmentioning

confidence: 96%

Critical behavior of certain antiferromagnets with complicated ordering: Four-loopɛ-expansion analysis

Mudrov

Varnashev

2001

Phys. Rev. B

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“…The functions Φ ± (u R ± ), given in equations (55) (8) [15] 2.2348 2.2663 2.0716 0.6300(15) [15] 24.56(10) [17] 2.2605 2.2956 2.0775 23.73 (8) 2.2178 2.2487 2.0570 0.624(2) [16] 24.56(10) 2.2431 2.2775 2.0630 expansion is analytic, which it is presumably not, but just take the different results as a measure for the error due to the shortness of the series. The application of Padé-Borel methods, which we also tried, does not yield any improvement.…”

Section: Expansion In U Rmentioning

confidence: 99%

“…Nickel, D.I. Meiron et al [8,9,10], who give the renormalization group functions and the critical exponents respectively up to six-and seven-loop order. Later C. Bagnuls, C. Bervillier et al [11,12] have developed a renormalization scheme, which among others makes it possible to determine the amplitude ratios of the susceptibility and the specific heat from these series.…”

Section: Introductionmentioning

confidence: 99%

Field-theoretic calculation of the universal amplitude ratio of correlation lengths in 3D Ising systems

Münster

Heitger

1994

Nuclear Physics B

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In three-dimensional systems of the Ising universality class the ratio of correlation length amplitudes for the high-and low-temperature phases is a universal quantity. Its field theoretic determination apart from the ǫ-expansion represents a gap in the existing literature. In this article we present a method, which allows to calculate this ratio by renormalized perturbation theory in the phases with unbroken and broken symmetry of a one-component φ 4 -theory in fixed dimensions D = 3. The results can be expressed as power series in the renormalized coupling constant of either of the two phases, and with the knowledge of their fixed point values numerical estimates are obtainable. These are given for the case of a two-loop calculation.

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“…the renormalization at zero momentum is performed using the following prescription for the two and four-point correlation functions of the eld : (2) …”

Section: Continuum Eld Theorymentioning

confidence: 99%

Four-point renormalized coupling constant in O(N) models

Campostrini

Pelissetto

Rossi

et al. 1996

Nuclear Physics B - Proceedings Supplements

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The renormalized zero-momentum four-point coupling gr of O(N)-invariant scalar eld theories in d dimensions is studied by applying the 1=N expansion and strong coupling analysis.The O(1=N) correction to the -function and to the xed point value g r are explictly computed. Strong coupling series for lattice non-linear models are analyzed near criticality in d = 2 and d = 3 for several values of N and the corresponding values of g r are extracted.Large-N and strong coupling results are compared with each other, nding a good general agreement. For small N the strong coupling analysis in 2-d gives the best determination of g r to date (or comparable for N = 2; 3 with the available Monte Carlo estimates), and in 3-d it is consistent with available 4 eld theory results.

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Ising-Model Critical Indices in Three Dimensions from the Callan-Symanzik Equation

Cited by 295 publications

References 15 publications

Critical behavior of certain antiferromagnets with complicated ordering: Four-loopɛ-expansion analysis

Critical behavior of certain antiferromagnets with complicated ordering: Four-loopɛ-expansion analysis

Field-theoretic calculation of the universal amplitude ratio of correlation lengths in 3D Ising systems

Four-point renormalized coupling constant in O(N) models

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