M. V. Komarova, M. Yu. Nalimov, “Asymptotic Behavior of Renormalization Constants in Higher Orders of the Perturbation Expansion for the $(4?\epsilon)$-Dimensionally Regularized $O(n)$-Symmetric $\phi^4$ Theory”, TMF, 126:3 (2001), 409–426; Theoret. and Math. Phys., 126:3 (2001), 339

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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 126, Number 3, Pages 409–426
DOI: https://doi.org/10.4213/tmf438 (Mi tmf438)

This article is cited in 21 scientific papers (total in 21 papers)

Asymptotic Behavior of Renormalization Constants in Higher Orders of the Perturbation Expansion for the

(4 ? ϵ)

$(4?\epsilon)$ -Dimensionally Regularized

O (n)

$O(n)$ -Symmetric

ϕ^{4}

$\phi^4$ Theory

M. V. Komarova, M. Yu. Nalimov

Saint-Petersburg State University

Full-text PDF (287 kB) Citations (21)

References:

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DOI: https://doi.org/10.4213/tmf438

Abstract: Higher-order asymptotic expansions for renormalization constants and critical exponents of the

O (n)

$O(n)$ -symmetric

ϕ^{4}

$\phi^4$ theory are found based on the instanton approach in the minimal subtraction scheme for the

(4 - ϵ)

$(4-\epsilon)$ -dimensional regularization. The exactly known expansion terms differ substantially from their asymptotic values. We find expressions that improve the asymptotic expansions for unknown expansion terms of the renormalization constants.

Received: 21.09.2000

English version:
Theoretical and Mathematical Physics, 2001, Volume 126, Issue 3, Pages 339–353
DOI: https://doi.org/10.1023/A:1010367917876

Bibliographic databases:

Language: Russian

Citation: M. V. Komarova, M. Yu. Nalimov, “Asymptotic Behavior of Renormalization Constants in Higher Orders of the Perturbation Expansion for the

(4 ? ϵ)

$(4?\epsilon)$ -Dimensionally Regularized

O (n)

$O(n)$ -Symmetric

ϕ^{4}

$\phi^4$ Theory”, TMF, 126:3 (2001), 409–426; Theoret. and Math. Phys., 126:3 (2001), 339–353

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf438

https://doi.org/10.4213/tmf438

https://www.mathnet.ru/eng/tmf/v126/i3/p409

This publication is cited in the following 21 articles:

Ella Ivanova, Georgii Kalagov, Marina Komarova, Mikhail Nalimov, “Quantum-Field Multiloop Calculations in Critical Dynamics”, Symmetry, 15:5 (2023), 1026
Paul-Hermann Balduf, “Statistics of Feynman amplitudes in ϕ4-theory”, J. High Energ. Phys., 2023:11 (2023)
Johan Henriksson, “The critical O(N) CFT: Methods and conformal data”, Physics Reports, 1002 (2023), 1
M. Yu. Nalimov, A. V. Ovsyannikov, “Convergent perturbation theory for studying phase transitions”, Theoret. and Math. Phys., 204:2 (2020), 1033–1045
McKane A.J., “Perturbation Expansions At Large Order: Results For Scalar Field Theories Revisited”, J. Phys. A-Math. Theor., 52:5 (2019), 055401
Gracey J.A., “Large N-F Quantum Field Theory”, Int. J. Mod. Phys. A, 33:35 (2018), 1830032
N. V. Antonov, M. V. Kompaniets, N. M. Lebedev, “Critical behavior of the $O(n)$ $\phi^4$ model with an antisymmetric tensor order parameter: Three-loop approximation”, Theoret. and Math. Phys., 190:2 (2017), 204–216
Kompaniets M.V. Panzer E., “Minimally Subtracted Six-Loop Renormalization of O(N)-Symmetric Phi(4) Theory and Critical Exponents”, Phys. Rev. D, 96:3 (2017), 036016
Kalagov G.A. Kompaniets M.V. Nalimov M.Yu., “Renormalization-group investigation of a superconducting U( r )-phase transition using five loops calculations”, Nucl. Phys. B, 905 (2016), 16–44
G. A. Kalagov, M. Yu. Nalimov, M. V. Kompaniets, “Renormalization-group study of a superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations”, Theoret. and Math. Phys., 181:2 (2014), 1448–1458
Kalagov G.A. Nalimov M.Yu., “Higher-Order Asymptotics and Critical Indexes in the Phi(3) Theory”, Nucl. Phys. B, 884 (2014), 672–683
Honkonen J., Komarova M.V., Nalimov M.Yu., “Bose–Einstein Condensation Beyond Perturbation Theory: Goldstone Singularities and Instanton Solution”, Eur. Phys. J. B, 87:3 (2014), 75
Komarova M.V., Kremnev I.S., Nalimov M.Yu., “Convergence of perturbation series for renormalization constants in Kraichnan model with “frozen” velocity field”, Eur Phys J C Part Fields, 71:5 (2011), 1646
M. Yu. Nalimov, V. A. Sergeev, L. Sladkoff, “Borel resummation of the $\varepsilon$-expansion of the dynamical exponent $z$ in model A of the $\phi^4(O(n))$ theory”, Theoret. and Math. Phys., 159:1 (2009), 499–508
Andreanov, AY, “Large-order asymptotes of the quantum-field expansions for the Kraichnan model of passive scalar advection”, Journal of Physics A-Mathematical and General, 39:25 (2006), 7801
M. V. Komarova, M. Yu. Nalimov, “Large-order asymptotic terms in perturbation theory: The first $(4-\epsilon)$-expansion correction to renormalization constants in the $O(n)$-symmetric theory”, Theoret. and Math. Phys., 143:2 (2005), 664–680
Honkonen, J, “Instantons for dynamic models from B to H”, Nuclear Physics B, 714:3 (2005), 292
Honkonen, J, “Large-order asymptotes for dynamic models near equilibrium”, Nuclear Physics B, 707:3 (2005), 493
Yukalov, VI, “Summation of power series by self-similar factor approximants”, Physica A-Statistical Mechanics and Its Applications, 328:3–4 (2003), 409
Honkonen, J, “Large order asymptotics and convergent perturbation theory for critical indices of the phi(4) model in 4 epsilon expansion”, Acta Physica Slovaca, 52:4 (2002), 303

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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