Scheme independence and the exact renormalization group

Ball, Richard D.; Haagensen, Peter E.; Latorre, José I.; Moreno, E.C.

doi:10.1016/0370-2693(95)00025-g

Cited by 118 publications

(256 citation statements)

References 25 publications

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“…On the other hand, both Γ Λ and the flow with k are scheme-dependent. The scheme dependence of the final results is a good check for approximations [8,87,88,89,90].…”

Section: The Functionalγmentioning

confidence: 99%

See 1 more Smart Citation

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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“…On the other hand, both Γ Λ and the flow with k are scheme-dependent. The scheme dependence of the final results is a good check for approximations [8,87,88,89,90].…”

Section: The Functionalγmentioning

confidence: 99%

“…As an example, for the critical exponent ν for N = 3 and η = 0 one finds ν = 0.74, to be compared with the known value ν = 0.71. (See also [87] for a discussion of the N = 1 case in three dimensions and section 4. )…”

Section: A Simple Example: the Quartic Potentialmentioning

confidence: 99%

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

2002

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“…In the case of scalar field theory, such a flow equation (withŜ I = 0) was first considered in [52]; the version with more general seed action has been considered in [47,53].…”

Section: Rescalingsmentioning

confidence: 99%

On the renormalization of theories of a scalar chiral superfield

Rosten

2010

J. High Energ. Phys.

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An exact renormalization group for theories of a scalar chiral superfield is formulated, directly in four dimensional Euclidean space. By constructing a projector which isolates the superpotential from the full Wilsonian effective action, it is shown that the nonperturbative nonrenormalization theorem follows, quite simply, from the flow equation. Next, it is argued that there do not exist any physically acceptable non-trivial fixed points. Finally, the Wess-Zumino model is considered, as a low energy effective theory. Following an evaluation of the one and two loop β-function coefficients, to illustrate the ease of use of the formalism, it is shown that the β-function in the massless case does not receive any nonperturbative power corrections. * Electronic address: orosten@stp.dias.ie 1 Contents

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“…Equation (10) guarantees that the regulator function is removed in the physical limit, where Γ ≡ lim k→0 Γ k . Equation (11) ensures that Γ k approaches the microscopic action S = lim k→Λ Γ k in the UV limit k → Λ.…”

Section: Renormalisation Group Flowsmentioning

confidence: 99%

“…For the computation of β-functions, this has been studied in [9]. More generally, and similar to perturbative QCD or truncations of Schwinger Dyson equations, approximate solutions of (1) depend spuriously on the IR regularisation [10][11][12][13][14][15][16]. A deeper understanding of the scheme dependence, and its link to the stability and convergence of the ERG flow, has been established recently [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Derivative expansion and renormalisation group flows

Litim

2001

J. High Energy Phys.

117

137

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We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better physical predictions. This is applied to O(N )-symmetric real scalar field theories in 3d, where critical exponents are computed for all N . In comparison to the sharp cut-off regulator, an optimised flow improves the leading order result up to 10%. An analogous reasoning is employed for a proper time renormalisation group. We compare our results with those obtained by other methods.

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Scheme independence and the exact renormalization group

Cited by 118 publications

References 25 publications

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

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

On the renormalization of theories of a scalar chiral superfield

Derivative expansion and renormalisation group flows

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