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For the three-dimensional cubic model, the nonlinear susceptibilities of thefourth, sixth, and eighth orders are analyzed and the parameters \delta^(i)characterizing their reduced anisotropy are evaluated at the cubic fixed point.In the course of this study, the renormalized sextic coupling constantsentering the small-field equation of state are calculated in the four-loopapproximation and the universal values of these couplings are estimated bymeans of the Pade-Borel-Leroy resummation of the series obtained. Theanisotropy parameters are found to be: \delta^(4) = 0.054 +/- 0.012, \delta^(6)= 0.102 +/- 0.02, and \delta^(8) = 0.144 +/- 0.04, indicating that theanisotropic (cubic) critical behavior predicted by the advanced higher-orderrenormalization-group analysis should be, in principle, visible in physical andcomputer experiments.Comment: 10 pages, LaTeX, no figures, published versio

Renormalization group and nonlinear susceptibilities of cubic ferromagnets at criticality