Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-10-12
Phys. Rev. E 60, 1344-1349 (1999)
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, LaTeX, no figures, published version with two wrongly addressed references in Table II capture corrected
Scientific paper
10.1103/PhysRevE.60.1344
The field-theoretical renormalization group approach in three dimensions is used to estimate the universal critical values of renormalized coupling constants g_6 and g_8 for the O(n)-symmetric model. The RG series for g_6 and g_8 are calculated in the four-loop and three-loop approximations respectively and then resummed by means of the Pade-Borel-Leroy technique. Under the optimal value of the shift parameter b providing the fastest convergence of the iteration procedure numerical estimates for the universal critical values g_6^*(n) are obtained for n = 1, 2, 3,...40 with the accuracy no worse than 0.3%. The RG expansion for g_8 demonstrates stronger divergence and results in considerably cruder numerical estimates. They are found to be consistent with the values of g_8^* deduced from the exact RG equations and, for n > 8, with those given by a constrained analysis of corresponding \epsilon-expansion.
Kashtanov S. S.
Orlov E. V.
Sokolov Aleksandr I.
Ul'kov V. A.
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