4 v 1 3 1 M ar 1 99 8 Critical exponents for 3 D O ( n ) – symmetric model with n > 3

Critical exponents for the 3D O(n)–symmetric model with n > 3 are estimated on the base of six–loop renormalisation–group (RG) expansions. Simple Padé–Borel technique is used for resummation of RG series and 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 critical exponents are also determined directly from six–loop expansions, without addressing to resummation procedure. Analysis of numbers obtained shows that resummation becomes unnecessary when n exceeds 28 provided an accuracy about 0.01 is adopted as satisfactory for gc and critical exponents. Further, results of the calculations performed are used to estimate numerical accuracy of the 1 n –expansion. The same value, n = 28, is shown to play a role of lower boundary of the domain where this approximation provides high–precision estimates for critical exponents.