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

Abstract

We report on a completely analytical calculation of the field anomalous dimension ${\gamma }_{\phi }$ and the critical exponent $\eta$ for the $O(n)$-symmetric ${\phi }^4$ model at the record six loop level. We successfully compare our result for ${\gamma }_{\phi }$ 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.

16 pages

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