najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-4-461-469najo-1025Research ArticleСтатьиRenormalization group in the infinite-dimensional turbulence: determination of the RG-functions without renormalization constantsAdzhemyanL. Ts.

Department of Theoretical Physics

Uljanovskaja 1, St. Petersburg, Petrodvorez, 198504

l.adzhemyan@spbu.ruKimT. L.

Department of Theoretical Physics

Uljanovskaja 1, St. Petersburg, Petrodvorez, 198504

KompanietsM. V.

Department of Theoretical Physics

Uljanovskaja 1, St. Petersburg, Petrodvorez, 198504

mkompan@gmail.comSazonovV. K.

Department of Theoretical Physics; Institute of Physics, Department of Theoretical Physics

Uljanovskaja 1, St. Petersburg, Petrodvorez, 198504

Universit¨atsplatz 5, A-8010 Graz

vasily.sazonov@uni-graz.atSt. Petersburg State UniversityRussian FederationSt. Petersburg State University; University of GrazRussian Federation20151608202564461469Copyright © Adzhemyan L.T., Kim T.L., Kompaniets M.V., Sazonov V.K., 20252025Adzhemyan L.T., Kim T.L., Kompaniets M.V., Sazonov V.K.Adzhemyan L.T., Kim T.L., Kompaniets M.V., Sazonov V.K.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1025

We calculate renormalization-group functions in the developed turbulence model for infinite dimensional space d → ∞ using an operating method without renormalization constants. The renormalization fixed point and index ω, obtained within the considered three loop approximation, are in agreement with previous calculations. The results demonstrate the efficiency of the method and the possibility of its complete automation, which is crucially important in higher order perturbation theory computations.

turbulencerenormalization group (RG)The work of LTsA, TLK and MVK was supported by Saint-Petersburg State University (project 11.38.185.2014). VKS acknowledges the support by the Austrian Science Fund FWF Grants Nr. I 1452-N27 and Nr. P21970-N16.The work of LTsA, TLK and MVK was supported by Saint-Petersburg State University (project 11.38.185.2014). VKS acknowledges the support by the Austrian Science Fund FWF Grants Nr. I 1452-N27 and Nr. P21970-N16.ReferencesM. Chertkov, G. Falkovich, I. Kolokolov, and V. Lebedev, Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar. Phys. Rev. E, 1995, 52, 4924. M. Chertkov and G. Falkovich, Anomalous Scaling Exponents of a White-Advected Passive Scalar. Phys. Rev. Lett., 1996, 76, P. 2706.M. Chertkov, G. Falkovich, I. Kolokolov, and V. Lebedev, Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar. Phys. Rev. E, 1995, 52, 4924. M. Chertkov and G. Falkovich, Anomalous Scaling Exponents of a White-Advected Passive Scalar. Phys. Rev. Lett., 1996, 76, P. 2706.J.-D. Fournier, U. Frisch, H. A. Rose. Infinite-dimensional turbulence. J. Phys. A, 11(1), 1978, P. 187– 198.J.-D. Fournier, U. Frisch, H. A. Rose. Infinite-dimensional turbulence. J. Phys. A, 11(1), 1978, P. 187– 198.L. Ts. Adzhemyan, N. V. Antonov, P. B. Gol’din, T. L. Kim and M. V. Kompaniets. Renormalization group in the infinite-dimensional turbulence: third-order results, Journal of Physics A: Mathematical and Theoretical, 2008, 41(49), P. 495002.L. Ts. Adzhemyan, N. V. Antonov, P. B. Gol’din, T. L. Kim and M. V. Kompaniets. Renormalization group in the infinite-dimensional turbulence: third-order results, Journal of Physics A: Mathematical and Theoretical, 2008, 41(49), P. 495002.L.Ts. Adzhemyan, N.V. Antonov, Renormalization group in turbulence theory: Exactly solvable Heisenberg model. Theoretical and Mathematical Physics, 115, 1098, P. 562–574.L.Ts. Adzhemyan, N.V. Antonov, Renormalization group in turbulence theory: Exactly solvable Heisenberg model. Theoretical and Mathematical Physics, 115, 1098, P. 562–574.L.Ts. Adzhemyan, M.V. Kompaniets, S.V. Novikov, V.K. Sazonov. Representation of the β-function and anomalous dimensions by nonsingular integrals: Proof of the main relation, Theoretical and Mathematical Physics, 2013, 175, P. 717–726.L.Ts. Adzhemyan, M.V. Kompaniets, S.V. Novikov, V.K. Sazonov. Representation of the β-function and anomalous dimensions by nonsingular integrals: Proof of the main relation, Theoretical and Mathematical Physics, 2013, 175, P. 717–726.L.Ts. Adzhemyan, M.V. Kompaniets, Five-loop numerical evaluation of critical exponents of the phi4 theory. Journal of Physics: Conference Series, 2014, 523, P. 012049.L.Ts. Adzhemyan, M.V. Kompaniets, Five-loop numerical evaluation of critical exponents of the phi4 theory. Journal of Physics: Conference Series, 2014, 523, P. 012049.P.C. Martin, E.D. Siggia, H.A. Rose. Statistical Dynamics of Classical Systems. Phys.Rev., 1973, A8, P. 423.P.C. Martin, E.D. Siggia, H.A. Rose. Statistical Dynamics of Classical Systems. Phys.Rev., 1973, A8, P. 423.A. N. Vasil’ev The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (Routledge Chapman & Hall 2004); ISBN 978-0-415-31002-4A. N. Vasil’ev The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (Routledge Chapman & Hall 2004); ISBN 978-0-415-31002-4O. I. Zavialov, Renormalized Quantum Field Theory, (Dordrecht :Kluwer, 1990).O. I. Zavialov, Renormalized Quantum Field Theory, (Dordrecht :Kluwer, 1990).

The authors declare that there are no conflicts of interest present.