Five-loop numerical evaluation of critical exponents of the $φ^4$ theory

We present a new approach to calculation of anomalous dimensions in the framework of $ε$-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 $ϕ^4$ model.

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