Scaling functions of susceptibilities toO(1/n) forn-vector models with axial anisotropy

For an axially anisotropicn-vector model withm = O(n) easy – andn – m = O(n) hard components of the order parameter, we derive the susceptibility r^–1 along one of the equivalent easy axes and the perpendicular one r^-1 toO(1/n) of the 1/n-expansion in the disordered phase. The results confirm predictions of the scaling theory, e.g.(g, t)=A t^–X (B g/t) and (g, t) =At^–X (B g/t), wheret = T – T_c(g = 0),g is the anisotropy parameter andX, X denote the scaling functions. We evaluate the relevant diagrams toO(1/n) which yield the coefficientsA, A and the critical behaviour of the scaling functions and critical amplitudes explicitly for. The extreme anisotropic case, i.e.m = O(1), is discussed briefly in the large-n limit in comparison with the mean field solution.Parts of this paper were presented at the Frühjahrstagung der Deutschen Physikalischen Gesellschaft in Freudenstadt (May 1974).