Convergence of the expansion of the renormalization group flow equation

Papp, Gábor; Schaefer, B.; Pirner, H. J.; Wambach, J.

doi:10.1103/physrevd.61.096002

Cited by 60 publications

(90 citation statements)

References 31 publications

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“…For details of the QCD aspects of this approach see the reviews [213] and [17] for a discussion of the phase diagram. Similar nonperturbative renormalization group studies of QCD motivated models can be found in [214,215,216]. Field theories with scalars and fermions have been investigated using similar techniques in [217,218,219,220].…”

Section: Introductionmentioning

confidence: 91%

Non-perturbative renormalization flow in quantum field theory and statistical physics

2002

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We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O(N )-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz-Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid-gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular we explore chiral symmetry breaking and the high temperature or high density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.This work is dedicated to the 60th birthday of Franz Wegner. *

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Section: Introductionmentioning

confidence: 91%

Non-perturbative renormalization flow in quantum field theory and statistical physics

2002

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“…From the explicit solutions (20) and (22) we deduce that α = −1 for the sharp cut-off, and α = 0 for the optimal regulator. Deriving the correct value for α from the large-n behaviour of a n seems to be the most difficult part of the reconstruction problem.…”

Section: From Erg To Ptrgmentioning

confidence: 99%

“…This set of functions is particularly important since it is the standard set used for analytical considerations [12,13] or numerical applications [20,24,25,26] of the PTRG. For m ≥ d 2 , this function satisfies the basic requirements imposed on f k (Λ, s).…”

Section: From Ptrg To Ergmentioning

confidence: 99%

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Predictive power of renormalisation group flows: a comparison

Litim

Pawlowski

2001

Physics Letters B

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We study a proper-time renormalisation group, which is based on an operator cut-off regularisation of the one-loop effective action. The predictive power of this approach is constrained because the flow is not an exact one. We compare it to the Exact Renormalisation Group, which is based on a momentum regulator in the Wilsonian sense. In contrast to the former, the latter provides an exact flow. To leading order in a derivative expansion, an explicit map from the exact to the proper-time renormalisation group is established. The opposite map does not exist in general. We discuss various implications of these findings, in particular in view of the predictive power of the proper-time renormalisation group. As an application, we compute critical exponents for O(N )-symmetric scalar theories at the Wilson-Fisher fixed point in 3d from both formalisms.

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“…From our numerical calculation shown in the next section, the symmetry restoration and meson mass spectra at finite temperature are not sensitive to the choice of the cutoff function [32].…”

Section: Application Of Functional Renormalization To Thementioning

confidence: 99%

Functional renormalization for chiral andUA(1)symmetries at finite temperature

Jiang

Zhuang

2012

Phys. Rev. D

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We investigated the chiral symmetry and UA(1) anomaly at finite temperature by applying the functional renormalization group to the SU (3) linear sigma model. Expanding the local potential around the classical fields, we derived the flow equations for the renormalization parameters. In chiral limit, the flow equation for the chiral condensate is decoupled from the others and can be analytically solved. The Goldstone theorem is guaranteed in vacuum and at finite temperature, and the two phase transitions for the chiral and UA(1) symmetry restoration happen at the same critical temperature. In general case with explicit chiral symmetry breaking, the two symmetries are partially and slowly restored, and the scalar and pseudoscalar meson masses are controlled by the restoration in the limit of high temperature.

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Convergence of the expansion of the renormalization group flow equation

Cited by 60 publications

References 31 publications

Non-perturbative renormalization flow in quantum field theory and statistical physics

Non-perturbative renormalization flow in quantum field theory and statistical physics

Predictive power of renormalisation group flows: a comparison

Functional renormalization for chiral andUA(1)symmetries at finite temperature

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