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”, TMF, 159:1 (2009), 96–108; Theoret. and Math. Phys., 159:1 (2009), 499

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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 1, Pages 96–108
DOI: https://doi.org/10.4213/tmf6335 (Mi tmf6335)

This article is cited in 18 scientific papers (total in 18 papers)

Borel resummation of the

ε

$\varepsilon$ -expansion of the dynamical exponent

z

$z$ in model A of the

ϕ^{4} (O (n))

$\phi^4(O(n))$ theory

M. Yu. Nalimov, V. A. Sergeev, L. Sladkoff

Saint-Petersburg State University

Full-text PDF (461 kB) Citations (18)

References:

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DOI: https://doi.org/10.4213/tmf6335

Abstract: We perform the Borel resummation of the currently known terms of the

ε

$\varepsilon$ -expansion up to order

ε^{4}

$\varepsilon^4$ of the dynamical exponent

z

$z$ in the critical-behavior model A. We obtain the large-order asymptotic approximation of the

ε

$\varepsilon$ -expansion of the dynamical exponent and find a significant discrepancy between the currently calculated orders of the expansion and the obtained asymptotic values. We discuss the influence of this deviation on the accuracy of the resummation results.

Keywords: Borel resummation, dynamical exponent, critical behavior, large-order asymptotic approximation.

Received: 11.08.2008

English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 1, Pages 499–508
DOI: https://doi.org/10.1007/s11232-009-0040-4

Bibliographic databases:

Language: Russian

Citation: M. Yu. Nalimov, V. A. Sergeev, L. Sladkoff, “Borel resummation of the

ε

$\varepsilon$ -expansion of the dynamical exponent

z

$z$ in model A of the

ϕ^{4} (O (n))

$\phi^4(O(n))$ theory”, TMF, 159:1 (2009), 96–108; Theoret. and Math. Phys., 159:1 (2009), 499–508

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf6335

https://doi.org/10.4213/tmf6335

https://www.mathnet.ru/eng/tmf/v159/i1/p96

This publication is cited in the following 18 articles:

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L. A. Gosteva, M. Yu. Nalimov, A. S. Yashugin, “Dynamical description of the phase transition to the superconducting state”, Theoret. and Math. Phys., 221:2 (2024), 1981–1993
Ella Ivanova, Georgii Kalagov, Marina Komarova, Mikhail Nalimov, “Quantum-Field Multiloop Calculations in Critical Dynamics”, Symmetry, 15:5 (2023), 1026
Adzhemyan L.Ts. Evdokimov D.A. Hnatic M. Ivanova V E. Kompaniets V M. Kudlis A. Zakharov V D., “The Dynamic Critical Exponent Z For 2D and 3D Ising Models From Five-Loop E Expansion”, Phys. Lett. A, 425 (2022), 127870
J. Honkonen, M. Komarova, Yu. Molotkov, M. Nalimov, A. Trenogin, “Critical dynamics of the superfluid phase transition: Multiloop calculation of the microscopic model”, Phys. Rev. E, 106:1 (2022)
L.Ts. Adzhemyan, D.A. Evdokimov, M. Hnatič, E.V. Ivanova, M.V. Kompaniets, A. Kudlis, D.V. Zakharov, “Model A of critical dynamics: 5-loop ɛ expansion study”, Physica A: Statistical Mechanics and its Applications, 600 (2022), 127530
V V Prudnikov, P V Prudnikov, E A Pospelov, A S Lyakh, “Simulation of non-equilibrium critical behavior of the 3D isotropic and anisotropic Heisenberg models”, J. Phys.: Conf. Ser., 1740:1 (2021), 012004
Honkonen J., Komarova V M., Molotkov Yu.G., Nalimov M.Yu., Zhavoronkov Yu.A., Mathematical Modeling and Computational Physics 2019 (Mmcp 2019), Epj Web of Conferences, 226, eds. Adam G., Busa J., Hnatic M., E D P Sciences, 2020
Yu. A. Zhavoronkov, M. V. Komarova, Yu. G. Molotkov, M. Yu. Nalimov, J. Honkonen, “Critical dynamics of the phase transition to the superfluid state”, Theoret. and Math. Phys., 200:2 (2019), 1237–1251
Adzhemyan L.Ts. Ivanova E.V. Kompaniets M.V. Vorobyeva S.Y., “Diagram Reduction in Problem of Critical Dynamics of Ferromagnets: 4-Loop Approximation”, J. Phys. A-Math. Theor., 51:15 (2018), 155003
Mera H. Pedersen T.G. Nikolic B.K., “Fast Summation of Divergent Series and Resurgent Transseries From Meijer-G Approximants”, Phys. Rev. D, 97:10 (2018), 105027
Zhong W., Barkema G.T., Panja D., Ball R.C., “Critical Dynamical Exponent of the Two-Dimensional Scalar Phi(4) Model With Local Moves”, Phys. Rev. E, 98:6 (2018), 062128
Lin Y., Wang F., “Linear Relaxation in Large Two-Dimensional Ising Models”, Phys. Rev. E, 93:2 (2016), 022113
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
M.V. Kompaniets, “Prediction of the higher-order terms based on Borel resummation with conformal mapping”, J. Phys.: Conf. Ser., 762 (2016), 012075
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
Samuel Friot, David Greynat, “Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin–Barnes Representation”, SIGMA, 6 (2010), 079, 23 pp.

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

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