Critical indices from perturbation analysis of the Callan-Symanzik equation

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

doi:10.1103/physrevb.17.1365

Cited by 453 publications

(338 citation statements)

References 27 publications

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“…(15)(16) represents the flow equation contribution from the three massless pions 3 , the middle term the sigma-meson contribution with mass squared term 2V ′ k +4φ 2 V ′′ k and the last term the N f N c quark contribution. 4 As a result of the choice of the cutoff function f (n) k for n > 1 (cf.…”

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

Convergence of the expansion of the renormalization group flow equation

et al. 2000

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We compare and discuss the dependence of a polynomial truncation of the effective potential used to solve exact renormalization group flow equation for a model with fermionic interaction (linear sigma model) with a grid solution. The sensitivity of the results on the underlying cutoff function is discussed. We explore the validity of the expansion method for second and first-order phase transitions.

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Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

Convergence of the expansion of the renormalization group flow equation

et al. 2000

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“…As it is known, the series of this type are asymptotic at best and a resummation procedure is to be applied in order to obtain reliable data on their basis. Here, we will make use of Padé-Borel resummation techniques [21] first writing the RG functions as resolvent However the applied procedure of resummation fails to give a correct description of β-functions for large negative w. In particular, in the region of couplings in the vicinity of FP VI we get real values of the β-functions and solution for m = 2 only. This is caused by the appearance of poles in integral rep-resentations of the resummed β-functions.…”

Section: Fixed Points and Their Stabilitymentioning

confidence: 99%

On the Critical Behaviour of Random Anisotropy Magnets

Dudka¹,

Folk²,

Holovatch³

2001

Condens. Matter Phys.

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The effect of a local anisotropy of random orientation on a ferromagnetic phase transition is studied. To this end, a model of a random anisotropy magnet is analysed by means of a field theoretical renormalization group approach. The one-loop result of Aharony about the absence of a 2nd order phase transition for isotropic distribution of random anisotropy axis at space dimension d < 4 is corroborated.

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“…In the scaling limit these functions are related to the amplitudes defined in eq. (8,11,15,25) as follows:…”

Section: Amplitude Ratiosmentioning

confidence: 99%

Universal amplitude ratios in the 3D Ising model

Caselle

Hasenbusch

1998

Nuclear Physics B - Proceedings Supplements

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We present a high precision Monte Carlo study of various universal amplitude ratios of the three dimensional Ising spin model. Using state of the art simulation techniques we studied the model close to criticality in both phases. Great care was taken to control systematic errors due to finite size effects and correction to scaling terms. We obtain C + /C − = 4.75(3), f +,2nd /f −,2nd = 1.95(2) and u * = 14.3(1). Our results are compatible with those obtained by field theoretic methods applied to the φ 4 theory and high and low temperature series expansions of the Ising model. The mismatch with a previous Montecarlo study by Ruge et al. remains to be understood. *

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Critical indices from perturbation analysis of the Callan-Symanzik equation

Cited by 453 publications

References 27 publications

Convergence of the expansion of the renormalization group flow equation

Convergence of the expansion of the renormalization group flow equation

On the Critical Behaviour of Random Anisotropy Magnets

Universal amplitude ratios in the 3D Ising model

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