Universal critical coupling constants for the three-dimensional n-vector model from field theory

Abstract

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 ε-expansion.

11 pages, LaTeX, no figures, published version with two wrongly addressed references in Table II capture corrected

References in corpus (7)

• Critical Exponents of the N-vector model
• Critical exponents for 3D O(n)-symmetric model with n > 3
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• Effective potential in three-dimensional O(N) models
• The 2n-point renormalized coupling constants in the 3d Ising model: estimates by high temperature series to order beta^17
• Universal sextic effective interaction at criticality
• Renormalized sextic coupling constant for the two-dimensional Ising model from field theory

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