Geodesic
Renormalization group and the $\varepsilon$-expansion: Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 1, pp. 100-111
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In the framework of the renormalization group and the $\varepsilon$-expansion, we propose expressions for the $\beta$-function and anomalous dimensions in terms of renormalized one-irreducible functions. These expressions are convenient for numerical calculations. We choose the renormalization scheme in which the quantities calculated using $R$ operations are represented by integrals that do not contain singularities in $\varepsilon$. We develop a completely automated calculation system starting from constructing diagrams, determining relevant subgraphs, combinatorial coefficients, etc., up to determining critical exponents. As an example, we calculate the critical exponents of the $\varphi^3$ model in the order $\varepsilon^4$.
Keywords: renormalization group, $\varepsilon$-expansion, multiloop diagrams, critical exponents. 
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     author = {L. Ts. Adzhemyan and M. V. Kompaniets},
     title = {Renormalization group and the~$\varepsilon$-expansion: {Representation} of the~$\beta$-function and anomalous dimensions by nonsingular integrals},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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L. Ts. Adzhemyan; M. V. Kompaniets. Renormalization group and the $\varepsilon$-expansion: Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 1, pp. 100-111. http://geodesic.mathdoc.fr/item/TMF_2011_169_1_a9/

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