Critical dynamics of ferromagnets in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>6</mml:mn><mml:mo>−</mml:mo><mml:mi>ε</mml:mi></mml:math>dimensions: General discussion and detailed calculation

Ma, Shang‐keng; Mazenko, Gene F.

doi:10.1103/physrevb.11.4077

Cited by 326 publications

(162 citation statements)

References 33 publications

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“…5.10.6 The DIA and stochastic particle acceleration Maasjost and Elsässer (1982) criticized the use of the DIA for the stochastic-acceleration problem on the grounds that it either agreed with much simpler Fokker-Planck theory or did not agree with simulation data. Their arguments were analyzed in detail by Dimits and Krommes (1986).…”

Section: Self-consistency and Polarization Effectsmentioning

confidence: 99%

“…The approach of Yakhot and Orszag (1986) 235 explicitly involves an additive random forcing described by a controversial (Lam, 1992) correspondence principle. Other methods that extend the work of Ma and Mazenko (1975) do not explicitly introduce the random forcing; see Zhou et al (1994) for further references. Eyink (1994) has clearly discussed the differences between various technical approaches to RG calculations.…”

Section: Renormalization-group Techniquesmentioning

confidence: 99%

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Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

260

397

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A pedagogical review of the historical development and current status (as of early 2000) of systematic statistical theories of plasma turbulence is undertaken. Emphasis is on conceptual foundations and methodology, not practical applications. Particular attention is paid to equations and formalism appropriate to strongly magnetized, fully ionized plasmas. Extensive reference to the literature on neutral-fluid turbulence is made, but the unique properties and problems of plasmas are emphasized throughout. Discussions are given of quasilinear theory, weak-turbulence theory, resonance-broadening theory, and the clump algorithm. Those are developed independently, then shown to be special cases of the direct-interaction approximation (DIA), which provides a central focus for the article. Various methods of renormalized perturbation theory are described, then unified with the aid of the generating-functional formalism of Martin, Siggia, and Rose. A general expression for the renormalized dielectric function is deduced and discussed in detail. Modern approaches such as decimation and PDF methods are described. Derivations of DIA-based Markovian closures are discussed. The eddy-damped quasinormal Markovian closure is shown to be nonrealizable in the presence of waves, and a new realizable Markovian closure is presented. The test-field model and a realizable modification thereof are also summarized. Numerical solutions of various closures for some plasmaphysics paradigms are reviewed. The variational approach to bounds on transport is developed. Miscellaneous topics include Onsager symmetries for turbulence, the interpretation of entropy balances for both kinetic and fluid descriptions, self-organized criticality, statistical interactions between disparate scales, and the roles of both mean and random shear. Appendices are provided on Fourier transform conventions, dimensional and scaling analysis, the derivations of nonlinear gyrokinetic and gyrofluid equations, stochasticity criteria for quasilinear theory, formal aspects of resonance-broadening theory, Novikov's theorem, the treatment of weak inhomogeneity, the derivation of the Vlasov weak-turbulence wave kinetic equation from a fully renormalized description, some features of a code for solving the direct-interaction approximation and related Markovian closures, the details of the solution of the EDQNM closure for a solvable three-wave model, and the notation used in the article.

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Section: Self-consistency and Polarization Effectsmentioning

confidence: 99%

Section: Renormalization-group Techniquesmentioning

confidence: 99%

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

260

397

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“…Because we are interested in a temperature region near the Curie temperature of the SI, where the Landau-Lifshitz-Gilbert equation with fixed magnetization size is invalid, we begin with the following time-dependent Ginzburg-Landau type equation 62 :…”

Section: Appendix B: Spin Pumping From Fluctuating Ferromagnetsmentioning

confidence: 99%

Enhanced dc spin pumping into a fluctuating ferromagnet nearTC

et al. 2014

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A linear-response formulation of the dc spin pumping, i.e., a spin injection from a precessing ferromagnet into an adjacent spin sink, is developed in view of describing many-body effects caused by spin fluctuations in the spin sink. It is shown that when an itinerant ferromagnet near TC is used as the spin sink, the spin pumping is largely with its Curie temperature located close to room temperature increased owing to the fluctuation enhancement of the spin conductance across the precessing ferromagnet/spin sink interface. As an example, the enhanced spin pumping from yttrium iron garnet into nickel palladium alloy (TC ≃ 20K) is analyzed by means of a self-consistent renormalization scheme, and it is predicted that the enhancement can be as large as tenfold.

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“…The first, (14), is known from statics. The second, (15), means that n·j α , the normal component of the current j α = −λ 0 (∇ δH δφ α + f 0 ǫ αβγ φ β ∇φ γ ), whose negative divergence gives the right-hand side of (10), vanishes at B. [The precession term yields a contribution ∝ ǫ αβγ φ β ∂ n φ γ which is zero by (14)].…”

mentioning

confidence: 99%

“…According to scaling considerations [13,14] and RG work [15,16], the dynamic bulk critical exponent z is given by…”

mentioning

confidence: 99%

Dynamic surface critical behavior of isotropic Heisenberg ferromagnets

Krech¹,

Karl²,

Diehl³

2001

Physica A: Statistical Mechanics and its Applications

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The effects of free surfaces on the dynamic critical behavior of isotropic Heisenberg ferromagnets are studied via phenomenological scaling theory, field-theoretic renormalization group tools, and high-precision computer simulations. An appropriate semi-infinite extension of the stochastic model J is constructed, the boundary terms of the associated dynamic field theory are identified, its renormalization in d ≤ 6 dimensions is clarified, and the boundary conditions it satisfies are given. Scaling laws are derived which relate the critical indices of the dynamic and static infrared singularities of surface quantities to familiar static bulk and surface exponents. Accurate computer-simulation data are presented for the dynamic surface structure factor; these are in conformity with the predicted scaling behavior and could be checked by appropriate scattering experiments.

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Critical dynamics of ferromagnets in6−εdimensions: General discussion and detailed calculation

Cited by 326 publications

References 33 publications

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Enhanced dc spin pumping into a fluctuating ferromagnet nearTC

Dynamic surface critical behavior of isotropic Heisenberg ferromagnets

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