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

Abstract

For an axially anisotropicn-vector model withm = O(n) easy − andn − m = O(n) hard components of the order parameter, we derive the susceptibilityχ ≡r ⁻¹ along one of the equivalent easy axes and the perpendicular oneχ _⊥ ≡r ^-1_⊥ toO(1/n) of the 1/n-expansion in the disordered phase. The results confirm predictions of the scaling theory, e.g.χ(g, t)=A t ^−γ X (B g/t ^ϕ) andχ _⊥ (g, t) =A _⊥ t ^−γ X _⊥ (B g/t ^ϕ), 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$r<< g^{\gamma /\phi }$. The extreme anisotropic case, i.e.m = O(1), is discussed briefly in the large-n limit in comparison with the mean field solution.