Universal effective coupling constants for the generalized Heisenberg model

The aim of this study is to find universal critical values of the effective dimensionless coupling constant g ₆ and refined universal values g ₄ for Heisenberg ferromagnets with n-component order parameters. These constants appear in the equation of state and determine the nonlinear susceptibilities χ ₄ and χ ₆ in the critical region. Calculations are made of the first three terms of the expansion of g ₆ in powers of g ₄ in the limits of O(n) symmetry three-dimensional λϕ ⁴ theory, the resultant series is resummed by the Padé-Borel method, and then by substituting the fixed point coordinates g ₄ ^* in the resultant expression, numerical values of g ₆ ^* are obtained for different n. These numbers g ₄ ^* for n>3 were determined from a six-loop expansion for the β-function resummed using the Padé-Borel-Leroy technique. An analysis of the accuracy of these g ₆ ^* values showed that they may differ from the true values by no more than 1.6%. These values of g ₆ ^* were compared with those obtained by the 1/n expansion method which allowed the level of accuracy of this method to be assessed. Fiz. Tverd. Tela (St. Petersburg) 40, 1284–1290 (July 1998)