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Theoretical and Mathematical Physics

, Volume 185, Issue 1, pp 1361–1369 | Cite as

Representation of the β-function and anomalous dimensions by nonsingular integrals in models of critical dynamics

  • L. Ts. AdzhemyanEmail author
  • S. E. Vorob’eva
  • M. V. Kompaniets
Article

Abstract

We propose a method for calculating the β-function and anomalous dimensions in critical dynamics models that is convenient for numerical calculations in the framework of the renormalization group and ε-expansion. Those quantities are expressed in terms of the renormalized Green’s function, which is renormalized using the operation R represented in a form that allows reducing ultraviolet divergences of Feynman diagrams explicitly. The integrals needed for the calculation do not contain poles in ε and are convenient for numerical integration.

Keywords

renormalization group ε-expansion multiloop diagram critical exponent 

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References

  1. 1.
    A. N. Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics [in Russian], PIYaF, St. Petersburg (1998); English transl., Chapman and Hall/CRC, Boca Raton, Fla. (2004).zbMATHCrossRefGoogle Scholar
  2. 2.
    K. G. Chetyrkin, A. L. Kataev, and F. V. Tkachev, Phys. Lett. B, 99, 147–150 (1981); Erratum, 101, 457–458 (1981)CrossRefGoogle Scholar
  3. 2.
    K. G. Chetyrkin, S. G. Gorishny, S. A. Larin, and F. V. Tkachov, Phys. Lett. B, 132, 351–354(1983); Preprint P-0453, Inst. Nucl. Res., Moscow (1986)CrossRefADSGoogle Scholar
  4. 2.
    D. I. Kazakov, Phys. Lett. B, 133, 406–410 (1983)CrossRefADSGoogle Scholar
  5. 2.
    D. I. Kazakov, Theor. Math. Phys., 58, 223–230 (1984)MathSciNetCrossRefGoogle Scholar
  6. 2.
    H. Kleinert, J. Neu, V. Shulte-Frohlinde, K. G. Chetyrkin, and S. A. Larin, Phys. Lett. B, 272, 39–44 (1991); Erratum, 319,545(1993).CrossRefADSGoogle Scholar
  7. 3.
    H.-K. Janssen and U. C. Täuber, Ann. Phys., 315, 147–192 (2005); arXiv:cond-mat/0409670v1 (2004).zbMATHCrossRefADSGoogle Scholar
  8. 4.
    N. V. Antonov and A. N. Vasil’ev, Theor. Math. Phys., 60, 671–679 (1984).CrossRefGoogle Scholar
  9. 5.
    L. Ts. Adzhemyan, A. N. Vasil’ev, Yu. S. Kabrits, and M. V. Kompaniets, Theor. Math. Phys., 119, 454–470 (1999).zbMATHMathSciNetCrossRefGoogle Scholar
  10. 6.
    L. Ts. Adzhemyan, N. V. Antonov, M. V. Kompaniets, and A. N. Vasil’ev, Internat. J. Mod. Phys. B, 17, 2137–2170 (2003).zbMATHCrossRefADSGoogle Scholar
  11. 7.
    L. Ts. Adzhemyan and M. V. Kompaniets, Theor. Math. Phys., 169, 1450–1459 (2011).zbMATHMathSciNetCrossRefGoogle Scholar
  12. 8.
    L. Ts. Adzhemyan, M. V. Kompaniets, S. V. Novikov, and V. K. Sazonov, Theor. Math. Phys., 175, 717–726 (2013).zbMATHMathSciNetCrossRefGoogle Scholar
  13. 9.
    L. Ts. Adzhemyan and M. V. Kompaniets, J. Phys.: Conf. Ser., 523,012049(2014); arXiv:1309.5621v1 [condmat. stat-mech] (2013).ADSGoogle Scholar
  14. 10.
    O. I. Zav’yalov, Renormalized Feynman Diagrams [in Russian], Nauka, Moscow (1979).Google Scholar
  15. 11.
    J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Intl. Ser. Monogr. Phys., Vol. 77), Oxford Univ. Press, Oxford (1989).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • L. Ts. Adzhemyan
    • 1
    Email author
  • S. E. Vorob’eva
    • 1
  • M. V. Kompaniets
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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