  The RG expansions for renormalized coupling constants g_6 and g_8 of the 3D
n-vector model are calculated in the 4-loop and 3-loop approximations
respectively. Resummation of the RG series for g_6 by the Pade-Borel-Leroy
technique results in the estimates for its universal critical values g_6^*(n)
which are argued to deviate from the exact numbers by less than 0.3%. The RG
expansion for g_8 demonstrates stronger divergence being much less suitable for
getting reliable numerical estimates.

High Energy Physics - Theory;Condensed Matter;High Energy Physics - Lattice;High Energy Physics - Phenomenology