Critical exponents from field theory

Guillou, J.C. Le; Zinn-Justin, Jean

doi:10.1103/physrevb.21.3976

Cited by 1,771 publications

(1,069 citation statements)

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“…The obtained value is consistent with predictions of the 3D − XY model, where ν = 0.67 and η = 0.03 [23]. The dynamics is described by the model E of Hohenberg and Halperin [24], where z = 1.5.…”

Section: Fluctuation Regimessupporting

confidence: 76%

Conductivity fluctuations of polycrystalline Ag-doped YBa2Cu3O7-δ superconductor

et al. 2010

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Systematic conductivity measurements near T C in granular Ag-doped YBa 2 Cu 3 O 7−δ superconductors are presented. Silver doped YBa 2 Cu 3 O 7−δ samples were produced by different routes and characterized by X-ray diffraction, dc magnetization and electrical resistivity. The results were analyzed in terms of the temperature derivative of the resistivity and of the logarithmic temperature derivative of the conductivity, that allowed identifying power-law divergences in the conductivity. The results show that the resistive transition proceeds in two stages. In the normal phase, Gaussian and critical fluctuation conductivity regimes were identified. Close to the zero-resistance temperature, a coherence transition related to the connective nature of the granular samples was evidenced. It was not observed significant differences in critical and Gaussian fluctuations between pure and Ag-doped YBa 2 Cu 3 O 7−δ polycrystalline samples.

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Section: Fluctuation Regimessupporting

confidence: 76%

Conductivity fluctuations of polycrystalline Ag-doped YBa2Cu3O7-δ superconductor

et al. 2010

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“…Best fits are obtained with α ≈ 2, which deviates from the standard value α =3/2 [17], and β ≈ 0.3, close to the theoretical value β = 0.325 for 3D Ising like ferromagnets [18]. The magnetization M(H) measured at 2 K in a field up to 5 T is shown in Fig.2 The temperature dependence of the electrical resistivity ρ(T) of the URh 1-x Co x Ge alloys is presented in Fig.3.…”

Section: Experimental Results and Analysismentioning

confidence: 99%

Ferromagnetic order in U(Rh, Co)Ge

Huy

Visser

2009

Solid State Communications

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Abstract:We report the variation of ferromagnetic order in the pseudo-ternary compounds URh 1-x Co x Ge (0 ≤ x ≤ 1). Magnetization and transport data taken on polycrystalline samples show that the Curie temperature T C gradually increases with increasing Co content from a value of 9.5 K for URhGe to a maximum value of 20 K for x = 0.6 and then steadily decreases to 3 K for UCoGe. The magnetic interaction strength varies smoothly across the series. For all samples the electrical resistivity for T < T C follows the behaviour ρ = ρ 0 + AT 2 . The A coefficient is dominated by scattering at spin waves and is strongly enhanced for x = 0 and 1.

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“…They have been extensively used to test RG predictions by comparing them with other results (experiments, high or low temperature series expansion, Monte-Carlo simulations) [13]. The first precise determination of the exponents of the O(N ) symmetric N -vector model has been reported by Le Guillou-ZinnJustin [1], using the six-loop series for RG functions calculated by Nickel et al [14]. The summation methods used in [1] were based on a Borel transformation and conformal map.…”

Section: Critical Exponents and Series Summationmentioning

confidence: 99%

“…The first precise determination of the exponents of the O(N ) symmetric N -vector model has been reported by Le Guillou-ZinnJustin [1], using the six-loop series for RG functions calculated by Nickel et al [14]. The summation methods used in [1] were based on a Borel transformation and conformal map. The same ideas have later been applied to the ε-expansion [15] when five loop series became available [16], and more recently to the equation of state by Guida-Zinn-Justin [3].…”

Section: Critical Exponents and Series Summationmentioning

confidence: 99%

“…We therefore review the methods, based on renormalized φ 4 3 quantum field theory and renormalization group, which have led to a precise determination of critical exponents of the N -vector model [1,2] and of the equation of state of the 3D Ising model [3]. These results are among the most precise available probing field theory in a nonperturbative regime.…”

Section: Introductionmentioning

confidence: 99%

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Precise determination of critical exponents and equation of state by field theory methods

Zinn-Justin¹

2001

Physics Reports

139

166

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Renormalization group, and in particular its Quantum Field Theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the methods, based on renormalized φ 4 3 quantum field theory and renormalization group, which have led to a precise determination of critical exponents of the N -vector model [1,2] and of the equation of state of the 3D Ising model [3]. These results are among the most precise available probing field theory in a nonperturbative regime.Precise calculations first require enough terms of the perturbative expansion. However perturbation series are known to be divergent. The divergence has been characterized by relating it to instanton contributions. The information about large order behaviour of perturbation series has then allowed to develop efficient "summation" techniques, based on Borel transformation and conformal mapping [4].We first discuss exponents and describe our recent results [2]. Compared to exponents, the determination of the scaling equation of state of the 3D Ising model involves a few additional (non-trivial) technical steps, like the use of the parametric representation, and the order dependent mapping method. From the knowledge of the equation of state a number of ratio of critical amplitudes can also be derived.Finally we emphasize that few physical quantities which are predicted by renormalization group to be universal have been determined precisely, and much work remains to be done. Considering the steady increase in the available computer Talk given at the Conference "Renormalization Group 2000, Taxco (Mexico), 11-15 Jan. 1999 * Laboratoire de la Direction des Sciences de la Matière du Commissariatà l'Energie Atomique 2 resources, many new calculations will become feasible. In addition to the infinite volume quantities, finite size universal quantities would also be of interest, to provide a more direct contact with numerical simulations. Let us also mention dynamical observables, a largely unexplored territory.

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Critical exponents from field theory

Cited by 1,771 publications

References 70 publications

Conductivity fluctuations of polycrystalline Ag-doped YBa2Cu3O7-δ superconductor

Conductivity fluctuations of polycrystalline Ag-doped YBa2Cu3O7-δ superconductor

Ferromagnetic order in U(Rh, Co)Ge

Precise determination of critical exponents and equation of state by field theory methods

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