Series expansion solution of the Wegner-Houghton renormalisation group equation

Margaritis, Athanasios; Ódor, Géza; Patkós, A.

doi:10.1007/bf01560398

Cited by 43 publications

(87 citation statements)

References 14 publications

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“…The solution to the last one seems, as far as we have investigated, to lead to convergence of previous solutions as M gets larger (see also [5]). …”

Section: Fixed Pointsmentioning

confidence: 80%

Gradient flows from an approximation to the exact renormalization group

Haagensen¹,

Kubyshin²,

Latorre³

et al. 1994

Physics Letters B

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Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in 2 < d < 4. The standard upper critical dimensions, k = 2, 3, 4, . . . appear naturally encoded in our formalism, and for dimensions smaller but very close to d k our results match the ǫ-expansion. Within the coupling constant subspace of mass and quartic couplings and for any d, we find a gradient flow with two fixed points determined by a positive-definite metric and a c-function which is monotonically decreasing along the flow.

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“…The solution to the last one seems, as far as we have investigated, to lead to convergence of previous solutions as M gets larger (see also [5]). …”

Section: Fixed Pointsmentioning

confidence: 80%

Gradient flows from an approximation to the exact renormalization group

Haagensen¹,

Kubyshin²,

Latorre³

et al. 1994

Physics Letters B

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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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“…It is expected that some properties, i.e., the scaling dimensions at the nontrivial fixed points, are universal and would not change very much under the enlargement if the approximation is good, while the others such as the directions of eigenvectors may change. It is well known that the restriction of the space of operators causes various artefacts [35,36,37].…”

Section: B Legendre Flow Equationmentioning

confidence: 99%

More About the Wilsonian Analysis on the Pionless Neft

Harada

Kubo

Ninomiya

2009

Int. J. Mod. Phys. A

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We extend our Wilsonian renormalization group (RG) analysis on the pionless nuclear effective theory (NEFT) in the two-nucleon sector in two ways; on the one hand, (1) we enlarge the space of operators up to including those of O(p 4 ) in the S waves, and, on the other hand, (2) we consider the RG flows in higher partial waves (P and D waves). In the larger space calculations, we find, in addition to nontrivial fixed points, two "fixed lines" and a "fixed surface" which are related to marginal operators. In the higher partial wave calculations, we find similar phase structures to that of the S waves, but there are two relevant directions in the P waves at the nontrivial fixed points and three in the D waves. We explain the physical meaning of the P -wave phase structure by explicitly calculating the low-energy scattering amplitude. We also discuss the relation between the Legendre flow equation which we employ and the RG equation by Birse, McGovern, and Richardson, and possible implementation of Power Divergence Subtraction (PDS) in higher partial waves.

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Series expansion solution of the Wegner-Houghton renormalisation group equation

Cited by 43 publications

References 14 publications

Gradient flows from an approximation to the exact renormalization group

Gradient flows from an approximation to the exact renormalization group

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

More About the Wilsonian Analysis on the Pionless Neft

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