Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO

Zolt\'an P\'eli

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Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO

Zoltán Péli

High Energy Physics - Theory · Submitted 8 Oct 2020

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

The authors' main claim We apply Wynn's epsilon algorithm to improve the predictions for the critical exponents, extrapolating beyond the next-to-next-to-leading order prediction of the derivative expansion.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,619 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.27 · mentions code or data availability 0.02.

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We apply the derivative expansion of the effective action in the exact renormalization group equation up to fourth order to the $Z_2$ and $O(N)$ symmetric scalar models in $d=3$ Euclidean dimensions. We compute the critical exponents $\nu$, $\eta$ and $\omega$ using polynomial expansion in the field. We obtain our predictions for the exponents employing two regulators widely used in ERG computations. We apply Wynn's epsilon algorithm to improve the predictions for the critical exponents, extrapolating beyond the next-to-next-to-leading order prediction of the derivative expansion.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We apply the derivative expansion of the effective action in the exact renormalization group equation up to fourth order to the $Z_2$ and $O(N)$ symmetric scalar models in $d=3$ Euclidean dimensions.	method 0.79	0.94	0.07	asserted 0.99
s1	We compute the critical exponents $\nu$, $\eta$ and $\omega$ using polynomial expansion in the field.	method 0.86	0.95	0.16	asserted 1.00
s2	We obtain our predictions for the exponents employing two regulators widely used in ERG computations.	method 0.97	0.93	0.07	asserted 1.00
s3	We apply Wynn's epsilon algorithm to improve the predictions for the critical exponents, extrapolating beyond the next-to-next-to-leading order prediction of the derivative expansion.	method 0.87	0.95	0.30	asserted 1.00

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Original abstract

We apply the derivative expansion of the effective action in the exact renormalization group equation up to fourth order to the $Z_2$ and $O(N)$ symmetric scalar models in $d=3$ Euclidean dimensions. We compute the critical exponents $\nu$, $\eta$ and $\omega$ using polynomial expansion in the field. We obtain our predictions for the exponents employing two regulators widely used in ERG computations. We apply Wynn's epsilon algorithm to improve the predictions for the critical exponents, extrapolating beyond the next-to-next-to-leading order prediction of the derivative expansion.

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3 arXiv papers cite this in 7 sentences

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This differs from more standard implementations of the DE [ref] .[Both versions of the DE give results for critical exponents that are compatible within error bars at order $O(∂^2)$ [ref] .] The details of the numerical solving of the equations is presented in Appendix [ref].

Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}(\partial^4)$ · The Derivative Expansion · 0.84

Cites it as support 1 paper

This has been confirmed by specific calculations of critical exponents in the Ising universality class at various orders up to order $𝒪(∂^6)$ [ref] for the Ising universality class, and up to order $𝒪(∂^4)$ for $O(N)$ models [ref] .[It is important to stress that the radius of convergence of order $q^2/k^2∼4$–$9$ only applies for an equation such as Eq. [ref] where only 1PI contributions are present.

Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}(\partial^4)$ · The Derivative Expansion · 0.96

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