Critical exponent $\eta$ in 2D $O(N)$-symmetric $\varphi^4$-model up to   6~loops
  Critical exponent $\eta$ (Fisher exponent) in $O(N)$-symmetric $\varphi^4$-model was calculated using renormalization group approach in the space of fixed dimension $D=2$ up to 6~loops. The calculation of the renormalization constants was performed with the use of $R'$-operation and specific values for diagrams were calculated in Feynman representation using sector decomposition method. Presented approach allows easy automation and generalization for the case of complex symmetries. Also a summation of the perturbation series was obtained by Borel transformation with conformal mapping. The contribution of the 6-th term of the series led to the increase of the Fisher exponent in $O(1)$ model up to $8\%$. 
L. Ts. Adzhemyan, Yu. V. Kirienko, M. V. Kompaniets
cond-mat.stat-mech