Scheme independence and the exact renormalization group

1994/11/30 by R. D. Ball, Richard D. Ball, P. E. Haagensen +5 · 125 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Critical dimension #Critical exponent #Cutoff #Functional renormalization group #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Order (exchange) #Renormalization #Renormalization group #Scalar (mathematics) #Scalar field theory #hep-th

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

published in Physics Letters B 347(1-2), 80-88 (Elsevier BV) · 15 pages, TeX with harvmac, 2 figures in compressed postscript; presentation of first section revised, several minor errors corrected, two references added

arxiv created 1994/12/08 · openalex publication_date 1995/03/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We compute critical exponents in a Z₂ symmetric scalar field theory in three dimensions, using Wilson's exact renormalization group equations expanded in powers of derivatives. A nontrivial relation between these exponents is confirmed explicitly at the first two orders in the derivative expansion. At leading order all our results are cutoff independent, while at next-to-leading order they are not, and the determination of critical exponents becomes ambiguous. We discuss the possible ways in which this scheme ambiguity might be resolved.

Citations

• The renormalization group and the ε expansion
• Critical exponents from the effective average action
• The renormalization group: Critical phenomena and the Kondo problem

Cited by

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• Polchinski equation, reparameterization invariance and the derivative expansion
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• Fate of nonpolynomial interactions in scalar field theory