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

S. A. Antonenko, A. I. Sokolov
1995 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated on the base of six-loop renormalization-group (RG) expansions. A simple Pade-Borel technique is used for the resummation of the RG series and the Pade approximants [L/1] are shown to give rather good numerical results for all calculated quantities. For large n, the fixed point location g_c and the critical exponents are also determined directly from six-loop expansions without addressing the resummation procedure. An
more » ... lysis 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 g_c and 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.
doi:10.1103/physreve.51.1894 pmid:9962848 fatcat:flux6n42ifbqbnfsjkxkmfo6xu