CRITICAL EXPONENTS FOR A 3-DIMENSIONAL O(N)-SYMMETRICAL MODEL WITH N-GREATER-THAN-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 gc 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 gc 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. © 1995 The American Physical Society.