Six loop analytical calculation of the field anomalous dimension and the critical exponent $\eta$ in $O(n)$-symmetric $\varphi^4$ model

TL;DR

This paper presents a six-loop analytical calculation of the field anomalous dimension and critical exponent in the $O(n)$-symmetric $^4$ model, extending previous loop order results and providing predictions for seven loops.

Contribution

The first complete six-loop analytical calculation of $ $-dependent $g$ and $$ in the $O(n)$-symmetric $^4$ model, with comparison to resummation predictions for $n=1$.

Findings

Agreement of $g$ for $n=1$ with Borel resummation predictions

Predictions for seven-loop contributions to $g$

Extension of loop order calculations to six loops

Abstract

We report on a completely analytical calculation of the field anomalous dimension $\gamma_{\varphi}$ and the critical exponent $\eta$ for the $O(n)$-symmetric $\varphi^4$ model at the record six loop level. We successfully compare our result for $\gamma_{\varphi}$ with $n=1$ with the predictions based on the method of the Borel resummation combined with a conformal mapping. Predictions for seven loop contribution to the field anomalous dimensions are given.