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TMF, 2013, Volume 175, Number 3, Pages 325–336 (Mi tmf8470)  

This article is cited in 5 scientific papers (total in 5 papers)

Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals: Proof of the main relation

L. Ts. Adzhemyana, M. V. Kompanietsa, S. V. Novikovb, V. K. Sazonova

a Saint Petersburg State University, St. Petersburg, Russia
b Google Switzerland GmbH, Zürich, Switzerland

Abstract: A method for calculating the $\beta$-function and anomalous dimensions, convenient for numerical calculations in the $\varepsilon$-expansion framework, was previously proposed, and the relation underlying the method was verified up to the four-loop approximation. We prove this relation in all orders of the perturbation theory.

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

DOI: https://doi.org/10.4213/tmf8470

Full text: PDF file (416 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2013, 175:3, 717–726

Bibliographic databases:

Document Type: Article
Received: 19.12.2012

Citation: L. Ts. Adzhemyan, M. V. Kompaniets, S. V. Novikov, V. K. Sazonov, “Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals: Proof of the main relation”, TMF, 175:3 (2013), 325–336; Theoret. and Math. Phys., 175:3 (2013), 717–726

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Adzhemyan L.Ts. Kompaniets M.V., “Five-Loop Numerical Evaluation of Critical Exponents of the Phi(4) Theory”, 15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Journal of Physics Conference Series, 523, IOP Publishing Ltd, 2014, 012049  crossref  isi  scopus
    2. 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”, Theoret. and Math. Phys., 185:1 (2015), 1361–1369  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Adzhemyan L.Ts., Hnatic M., Kompaniets M., Lucivjansky T., Mizisin L., “Numerical Calculation of Scaling Exponents of Percolation Process in the Framework of Renormalization Group Approach”, Mathematical Modeling and Computational Physics (MMCP 2015), EPJ Web of Conferences, 108, ed. Adam G. Busa J. Hnatic M., EDP Sciences, 2016, 02005  crossref  mathscinet  isi  scopus
    4. Adzhemyan L.Ts., Hnatic M., Kompaniets M.V., Luoivjansky T., Mizisin L., “Directed Percolation: Calculation of Feynman Diagrams in the Three-Loop Approximation”, Mathematical Modeling and Computational Physics 2017 (Mmcp 2017), Epj Web of Conferences, 173, eds. Adam G., Busa J., Hnatic M., Podgainy D., E D P Sciences, 2018, UNSP 02001  crossref  isi  scopus
    5. 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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