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

Understand

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 $\phi^4$ model.