Effective action for the chiral quark-meson model

Jungnickel, D.-U.; Wetterich, C.

doi:10.1103/physrevd.53.5142

Cited by 198 publications

(372 citation statements)

References 61 publications

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“…An important property will be the observation that certain low energy properties are effectively independent of the details of the model even away from the phase transition. This behavior is caused by a strong attraction of the renormalization group flow to approximate partial infrared fixed points [167,28]. Within this approach at high density we find [212] a chiral symmetry restoring first order transition.…”

Section: Introductionmentioning

confidence: 85%

“…It is convenient to introduce two-parameter functions l d n 1 ,n 2 (w 1 , w 2 ; η) [167]. For n 1 = n 2 = 1 their relation to the functions l d n (w; η) can be expressed as…”

Section: Scaling Form Of the Flow Equationsmentioning

confidence: 99%

“…ψ ψ ≃ 0, which signals the chiral phase transition. We will investigate the chiral phase transition within the linear quark meson model [167] for two quark flavors. Truncated nonperturbative flow equations are derived at nonzero temperature [28] and chemical potential [212].…”

Section: Introductionmentioning

confidence: 99%

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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: 85%

“…It is convenient to introduce two-parameter functions l d n 1 ,n 2 (w 1 , w 2 ; η) [167]. For n 1 = n 2 = 1 their relation to the functions l d n (w; η) can be expressed as…”

Section: Scaling Form Of the Flow Equationsmentioning

confidence: 99%

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

2002

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“…This situation arises during the study of the phase diagram of QCD at non-zero temperature T and baryonic chemical potential µ [1,23,24,25]. An effective theory that captures many of the features of QCD is the quark-meson model [22]. It employs mesons and quarks as physical degrees of freedom.…”

Section: The Renormalization-group Flowmentioning

confidence: 99%

“…The full QCD dynamics cannot be described by an effective Lagrangian involving only mesonic fields. More complicated effective descriptions, such as the linear quark-meson model, have been used for the discussion of the phase diagram for low chemical potential [22,23,24]. In ref.…”

Section: Introductionmentioning

confidence: 99%

The universal equation of state near the critical point of QCD

Brouzakis¹,

Tetradis²

2004

Nuclear Physics A

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We study the universal properties of the phase diagram of QCD near the critical point using the exact renormalization group. For two-flavour QCD and zero quark masses we derive the universal equation of state in the vicinity of the tricritical point. For non-zero quark masses we explain how the universal equation of state of the Ising universality class can be used in order to describe the physical behaviour near the line of critical points. The effective exponents that parametrize the growth of physical quantities, such as the correlation length, are given by combinations of the critical exponents of the Ising class that depend on the path along which the critical point is approached. In general the critical region, in which such quantities become large, is smaller than naively expected.

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Nonperturbative Flow Equations, Low-Energy QCD, and the Chiral Phase Transition

Jungnickel

Wetterich

NATO Science Series: B:

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We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. This is applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of the chiral phase transition in two flavor QCD. A precision estimate of the universal critical equation of state for the three-dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near T c turns out to be smaller than its zero temperature value.

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Effective action for the chiral quark-meson model

Cited by 198 publications

References 61 publications

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

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

The universal equation of state near the critical point of QCD

Nonperturbative Flow Equations, Low-Energy QCD, and the Chiral Phase Transition

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