Universal critical coupling constants for the three-dimensional n-vector model from field theory

The field-theoretical renormalization group (RG) approach in three dimensions is used to estimate the universal critical values of renormalized coupling constants g6 and g8 for the O(n)-symmetric model. The RG series for g6 and g8 are calculated in the four- and three-loop approximations, respectively, and then resummed by means of the Padé-Borel-Leroy technique. Under the optimal value of the shift parameter b providing the fastest convergence of the iteration procedure, numerical estimates for g*6 are obtained with an accuracy no worse than 0.3%. The RG expansion for g8 demonstrates a stronger divergence, and results in considerably cruder numerical estimates.