Geodesic
Representation of the~$\beta$-function and anomalous dimensions by nonsingular integrals in models of critical dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 3-11

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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. 
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     author = {L. Ts. Adzhemyan and S. E. Vorobyeva and M. V. Kompaniets},
     title = {Representation of the~$\beta$-function and anomalous dimensions by nonsingular integrals in models of critical dynamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {185},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a0/}
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a0/