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TMF, 2015, Volume 185, Number 1, Pages 3–11 (Mi tmf8911)  

This article is cited in 1 scientific paper (total in 1 paper)

Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals in models of critical dynamics

L. Ts. Adzhemyan, S. E. Vorobyeva, M. V. Kompaniets

St. Petersburg State University, St. Petersburg, Russia

Abstract: We propose a method for calculating the $\beta$-function and anomalous dimensions in critical dynamics models that is convenient for numerical calculations in the framework of the renormalization group and $\varepsilon$-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 $\varepsilon$ and are convenient for numerical integration.

Keywords: renormalization group, $\varepsilon$-expansion, multiloop diagram, critical exponent

Funding Agency Grant Number
Saint Petersburg State University 11.38.185.2014


DOI: https://doi.org/10.4213/tmf8911

Full text: PDF file (366 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 185:1, 1361–1369

Bibliographic databases:

Document Type: Article

Citation: L. Ts. Adzhemyan, S. E. Vorobyeva, M. V. Kompaniets, “Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals in models of critical dynamics”, TMF, 185:1 (2015), 3–11; Theoret. and Math. Phys., 185:1 (2015), 1361–1369

Citation in format AMSBIB
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\by L.~Ts.~Adzhemyan, S.~E.~Vorobyeva, M.~V.~Kompaniets
\paper Representation of the~$\beta$-function and anomalous dimensions by nonsingular integrals in models of critical dynamics
\jour TMF
\yr 2015
\vol 185
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\pages 3--11
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\jour Theoret. and Math. Phys.
\yr 2015
\vol 185
\issue 1
\pages 1361--1369
\crossref{https://doi.org/10.1007/s11232-015-0345-4}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. Ts. Adzhemyan, S. E. Vorob'eva, E. V. Ivanova, M. V. Kompaniets, “Representation of renormalization group functions by nonsingular integrals in a model of the critical dynamics of ferromagnets: The fourth order of the $\varepsilon$-expansion”, Theoret. and Math. Phys., 195:1 (2018), 584–594  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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