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This article is cited in 17 scientific papers (total in 17 papers)
Renormalization group and the $\varepsilon$-expansion: Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals
L. Ts. Adzhemyan, M. V. Kompaniets Saint Petersburg State University, St.~Petersburg, Russia
Abstract:
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.
Received: 20.10.2011
Citation:
L. Ts. Adzhemyan, M. V. Kompaniets, “Renormalization group and the $\varepsilon$-expansion: Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals”, TMF, 169:1 (2011), 100–111; Theoret. and Math. Phys., 169:1 (2011), 1450–1459
Linking options:
https://www.mathnet.ru/eng/tmf6712https://doi.org/10.4213/tmf6712 https://www.mathnet.ru/eng/tmf/v169/i1/p100
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Abstract page: | 621 | Full-text PDF : | 241 | References: | 84 | First page: | 14 |
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