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

We report on a completely analytical calculation of the field anomalous dimension $γ_φ$ and the critical exponent $η$ for the $O(n)$-symmetric $φ^4$ model at the record six loop level. We successfully compare our result for $γ_φ$ 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.

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