Five-loop renormalization group functions of ${O}(n)$-symmetric $\phi^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$

TL;DR

This paper provides a complete recalculation of five-loop renormalization group functions for the ${O}(n)$-symmetric $^4$-theory, correcting previous errors and extending $ ext{epsilon}$-expansions of critical exponents to fifth order.

Contribution

It presents the first full analytic reevaluation of all five-loop diagrams for the model, correcting prior inaccuracies and providing higher-order $ ext{epsilon}$-expansions of critical exponents.

Findings

Corrected five-loop $eta$-function and anomalous dimensions.

Extended $ ext{epsilon}$-expansions of critical exponents to $ ext{epsilon}^5$.

Validated the consistency of the revised calculations.

Abstract

Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the $\beta$-function and the anomalous dimensions of the ${O}(n)$-symmetric $\phi^4$-theory in $D=4-\ep$ dimensions we present the results of a full analytic reevaluation of all diagrams. The divergences are removed by minimal subtraction and $\ep$-expansions are given for the critical exponents $\eta$, $\nu$, and $\omega$ up to order $\epsilon^5$.