Gradient flows from an approximation to the exact renormalization group

Haagensen, Peter E.; Kubyshin, Yu. A.; Latorre, José I.; Moreno, E.C.

doi:10.1016/0370-2693(94)91228-9

Cited by 36 publications

(57 citation statements)

References 14 publications

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“…The flow (5.16) is similar to the one given in [9], which was there found "by trial and error". Equation (5.16) is the first non-trivial example of explicit flow equation for the c-function obtained using the procedure presented in this work.…”

Section: Jhep07(2014)040supporting

confidence: 74%

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A functional RG equation for the c-function

Codello

D'Odorico

Pagani

2014

J. High Energ. Phys.

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Abstract:After showing how to prove the integrated c-theorem within the functional RG framework based on the effective average action, we derive an exact RG flow equation for Zamolodchikov's c-function in two dimensions by relating it to the flow of the effective average action. In order to obtain a non-trivial flow for the c-function, we will need to understand the general form of the effective average action away from criticality, where nonlocal invariants, with beta functions as coefficients, must be included in the ansatz to be consistent. Then we apply our construction to several examples: exact results, local potential approximation and loop expansion. In each case we construct the relative approximate c-function and find it to be consistent with Zamolodchikov's c-theorem. Finally, we present a relation between the c-function and the (matter induced) beta function of Newton's constant, allowing us to use heat kernel techniques to compute the RG running of the c-function.

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Section: Jhep07(2014)040supporting

confidence: 74%

“…A scale derivative of (3.8) gives: 9) JHEP07 (2014)040 in which the expectation values are calculated with the fRG-regularized path integral. Using the fact that the Legendre transform of the generator of connected correlation functions is Γ k + ∆S k , we have:…”

Section: Jhep07(2014)040mentioning

confidence: 99%

A functional RG equation for the c-function

Codello

D'Odorico

Pagani

2014

J. High Energ. Phys.

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“…22 See also [103,104] for the importance of expanding around Φ = Φ 0 instead of Φ = 0 and refs. [105,106,107].…”

Section: Truncationsmentioning

confidence: 99%

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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“…The exciting competition for the 'best' critical exponents have led to several works using this method [24], [53], [17], [50], [51], [25], [57], [26]. Such kind of application opens up the issue of understanding the impact of truncation on the blocking [27], [28], [29] [25], [30], [31] and looking for optimization [32], [33], [18]. The phase structure and the nature of phase transitions are natural subjects [21], [34], [35].…”

Section: Applicationsmentioning

confidence: 99%

Lectures on the functional renormalization group method

Polónyi¹

2003

Open Physics

229

202

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These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum eld theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained by a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed brie®y as an alternative way to arrive at the renormalization group equation. The scaling laws and xed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The ®attening of the e¬ective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.

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Gradient flows from an approximation to the exact renormalization group

Cited by 36 publications

References 14 publications

A functional RG equation for the c-function

A functional RG equation for the c-function

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

Lectures on the functional renormalization group method

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