Scheme Independence and the Exact Renormalization Group

E. Moreno; J.I. Latorre; P.E. Haagensen; R. D. Ball

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Scheme Independence and the Exact Renormalization Group

R. D. Ball, P.E. Haagensen, J.I. Latorre, E. Moreno

High Energy Physics - Theory · Submitted 16 Nov 1994

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv IDhep-th/9411122 (version 3)

Pith IDDNPTDALU, Pith's permanent record of this paper and its review

CitationE. Moreno, J.I. Latorre, P.E. Haagensen, R. D. Ball. "Scheme Independence and the Exact Renormalization Group." arXiv:hep-th/9411122 (1994). https://pith.science/paper/DNPTDALU

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.96 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.15 · mentions code or data availability 0.02.

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We compute critical exponents in a $Z_2$ 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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute critical exponents in a $Z_2$ symmetric scalar field theory in three dimensions, using Wilson's exact renormalization group equations expanded in powers of derivatives.	contribution 0.62	0.96	0.06	asserted 1.00
s1	A nontrivial relation between these exponents is confirmed explicitly at the first two orders in the derivative expansion.	result 1.00	0.89	0.25	asserted 1.00
s2	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.	limitation 0.59	0.93	0.59	asserted 1.00
s3	We discuss the possible ways in which this scheme ambiguity might be resolved.	future work 0.52	0.46	0.08	speculative 0.41

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.57.

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The paper

Original abstract

We compute critical exponents in a $Z_2$ 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.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Maximising the minimum of the coarse-grained inverse propagator over regulator choices selects a preferred class of coarse-grainings, with optimal value 2, and explains why the sharp cutoff converges poorly.
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Fundamentals of the Exact Renormalization Group
hep-th 2010-03 conditional novelty 6.0 of 10

The review organizes Exact Renormalization Group methods and argues, via a dual-action construction, that the anomalous dimension at critical fixed points takes only discrete values.
Introduction to the functional RG and applications to gauge theories
hep-ph 2006-11 unverdicted novelty 2.0 of 10

The paper is a pedagogical introduction to functional renormalization group methods for gauge theories, not a report of a new research result.

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9 arXiv papers cite this in 21 sentences

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Papers citing it · 16 sentences without a confident label

Uses its method or tool 1 paper

In practice[ The reasoning of Ball et al is different but it is more convenient, and equivalent, to present it that way.], instead of considering $S_int$, Ball et al [ref] have chosen to perform the above change $d_ϕ^( c)$by $d_ϕ^( -)$ within the flow equation of the full action $S[ ϕ̃,t]$ (<ref>) which then reads: [equation]

Structure of Exact Renormalization Group Equations for field theory · Field-renormalization: the “modified” Polchinski ERGE · 0.85

Compares with it 2 papers

Notice that this condition is independent of the choice of the cutoff function, contrary to what is observed with the complete $O( ∂^2)$-order [ref] (for another difference with the complete order, see footnote [ref]).

Revisiting the local potential approximation of the exact renormalization group equation · Pseudo-LPA · 0.90
Indeed, ([ref]) is the flow equation for $S$ as obtained by Ball et al [ref] , using the analytical method sketched in section <ref>, but in which the field-renormalization step is implemented via $𝒪_P( S,ϕ̃)$ instead of being implemented linearly within $𝒢_dil$ exclusively.

Structure of Exact Renormalization Group Equations for field theory · Structural derivation · 0.89

Cites it as background 2 papers

Beyond the determinations of the critical exponent $ν$ in the LPA, great efforts have been made to determine $ν$ and $η$ in the NLO of the GE taking with the evolution of either the uniform (NLOu) [ref] or the field-dependent (NLOf) [ref] wavefunction renormalization.

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models · Short overview on the present status of the determination of the critical exponents of the WF FP in the functional RG fr · 0.91
Section ([ref]) shows how these latter two steps have been currently implemented to give the so-called “modified” Polchinski ERGE [ref] .

Structure of Exact Renormalization Group Equations for field theory · Introduction · 0.81

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