Accurate critical exponents from the optimal truncation of the ε-expansion within the O(N)-symmetric field theory for large N.
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| Title: | Accurate critical exponents from the optimal truncation of the ε-expansion within the O(N)-symmetric field theory for large N. |
|---|---|
| Authors: | Shalaby, Abouzeid M.1 (AUTHOR) amshalab@qu.edu.qa |
| Source: | European Physical Journal C -- Particles & Fields. Jul2025, Vol. 85 Issue 7, p1-10. 10p. |
| Subjects: | Critical exponents, Renormalization (Physics), Field theory (Physics), Padé approximant, Statistical models, Perturbation theory |
| Abstract: | The perturbation series for the renormalization group functions of the O(N)-symmetric ϕ 4 field theory are divergent but asymptotic. They are usually followed by Resummation calculations to extract reliable results. Although the same features exist for QED series, their partial sums can return accurate results because the perturbation parameter is small. In this work, however, we show that, for N ≥ 4 , the partial sum (according to optimal truncation) of the series for the exponents ν and η gives results that are very competitive to the recent Monte Carlo, Non-perturbative Renormalization group and Conformal field calculations. The order at which the series is truncated is inversely proportional to α = σ ε = 3 ε N + 8 which is higher for larger N while the error is smaller. Thus as N increases one expects accurate perturbative results like the QED case. Such optimal truncation, however, doesn't work for the series of the critical exponent ω (for intermediate values of N) as the truncated series includes only the first order. Nevertheless, for N ≥ 4 , the large-order parameter σ = 3 N + 8 is getting smaller which rationalizes for the use of Pad e ´ approximation. For that aim, we first obtain the seven-loop ε -series from the recent available corresponding g-expansion. The seven-loop Pad e ´ approximation gives accurate results for the three exponents. Besides, for all the seven orders in the series, the large-N limit leads to the exact result predicted by the non-perturbative 1/N-expansion. [ABSTRACT FROM AUTHOR] |
| Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Header | DbId: egs DbLabel: Engineering Source An: 187406268 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Accurate critical exponents from the optimal truncation of the ε-expansion within the O(N)-symmetric field theory for large N. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Shalaby%2C+Abouzeid+M%2E%22">Shalaby, Abouzeid M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> amshalab@qu.edu.qa</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. Jul2025, Vol. 85 Issue 7, p1-10. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Critical+exponents%22">Critical exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Renormalization+%28Physics%29%22">Renormalization (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Field+theory+%28Physics%29%22">Field theory (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Padé+approximant%22">Padé approximant</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The perturbation series for the renormalization group functions of the O(N)-symmetric ϕ 4 field theory are divergent but asymptotic. They are usually followed by Resummation calculations to extract reliable results. Although the same features exist for QED series, their partial sums can return accurate results because the perturbation parameter is small. In this work, however, we show that, for N ≥ 4 , the partial sum (according to optimal truncation) of the series for the exponents ν and η gives results that are very competitive to the recent Monte Carlo, Non-perturbative Renormalization group and Conformal field calculations. The order at which the series is truncated is inversely proportional to α = σ ε = 3 ε N + 8 which is higher for larger N while the error is smaller. Thus as N increases one expects accurate perturbative results like the QED case. Such optimal truncation, however, doesn't work for the series of the critical exponent ω (for intermediate values of N) as the truncated series includes only the first order. Nevertheless, for N ≥ 4 , the large-order parameter σ = 3 N + 8 is getting smaller which rationalizes for the use of Pad e ´ approximation. For that aim, we first obtain the seven-loop ε -series from the recent available corresponding g-expansion. The seven-loop Pad e ´ approximation gives accurate results for the three exponents. Besides, for all the seven orders in the series, the large-N limit leads to the exact result predicted by the non-perturbative 1/N-expansion. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1140/epjc/s10052-025-14473-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 1 Subjects: – SubjectFull: Critical exponents Type: general – SubjectFull: Renormalization (Physics) Type: general – SubjectFull: Field theory (Physics) Type: general – SubjectFull: Padé approximant Type: general – SubjectFull: Statistical models Type: general – SubjectFull: Perturbation theory Type: general Titles: – TitleFull: Accurate critical exponents from the optimal truncation of the ε-expansion within the O(N)-symmetric field theory for large N. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Shalaby, Abouzeid M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 14346044 Numbering: – Type: volume Value: 85 – Type: issue Value: 7 Titles: – TitleFull: European Physical Journal C -- Particles & Fields Type: main |
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