Critical Coupling, critical exponents ω andη from the eight-loop series for the O(N)-symmetric Φ⁴ Field theory

In Eur. Phys. J. C (2021) 81:87, we applied our hypergeometric-Meijer algorithm to extract accurate critical exponents for the second order phase transition in the O(N)-symmetric Φ⁴ field theory. Very recently, Oliver Schnetz obtained the eight-loop series for the anomalous field dimension γ_Φ renormalization group function. Both the seven-loop β-function and γ_Φ are up 8th order in the renormalized coupling g. It is a matter of fact that the ε-expansion gives better prediction than the g-series and it would be more Illustrative to test the accuracy of the 8th order g-series. We stressed the calculation of the critical exponents based on the eight-loop g-series for N=0,1,2,3 and 4 where accurate results are obtained.