Critical exponents for a three-dimensional O(n)-symmetric model withn>3

Critical exponents for the three-dimensional O(n)-symmetric model with n>3 are estimated on the basis of six-loop renormalization-group (RG) expansions. A simple Padé-Borel technique is used for the resummation of the RG series and the Padé approximants [L/1] are shown to give rather good numerical results for all calculated quantities. For large n, the fixed point location ${\mathit{g}}_{\mathit{c}}$ and the critical exponents are also determined directly from six-loop expansions without addressing the resummation procedure. An analysis of the numbers obtained shows that resummation becomes unnecessary when n exceeds 28 provided an accuracy of about 0.01 is adopted as satisfactory for ${\mathit{g}}_{\mathit{c}}$ and the critical exponents. Further, results of the calculations performed are used to estimate the numerical accuracy of the 1/n expansion. The same value n=28 is shown to play the role of the lower boundary of the domain where this approximation provides high-precision estimates for the critical exponents.