Five-loop numerical evaluation of critical exponents of the ${\phi }^4$ theory

Abstract

We present a new approach to calculation of anomalous dimensions in the framework of $\epsilon$-expansion and renormalization group method. This approach allows one to skip the calculation of renormalization constants and express anomalous dimensions in terms of renormalized diagrams, which are presented in a form suitable for numerical calculations. This approach can be easily automated and extended to a wide range of models. The power of this approach is illustrated on 5 loop calculations of beta-function and anomalous dimensions in ${\varphi }^4$ model.

8 pages, 5 figures. To be submitted to the proceedings of ACAT 2013

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