Scaling function for order-parameter correlations in expansion to order 1/n

The order-parameter correlation function Ĝ(q, ξ1) is calculated in the critical region of momentum space q in terms of a second-moment correlation length ξ1 by means of perturbation expansion to order 1/n, for an n-vector system with short-range interactions, in zero field above Tc, for 2 < d < 4. The scaling function of the q dependence is obtained in closed form with a precisely identified cutoff-dependent factor which is the amplitude of the correlation-length dependence of the susceptibility. Both the exponents and the coefficients of the expansion for fixed q as t = (T−Tc)/Tc → 0 are given explicitly and the former are shown to be in accordance with the operator product expansion. The coefficients of order 1/n in the terms associated with a tk(1−α) dependence of the energy density, for integer k ≥ 1, are expected to be explicitly cutoff-dependent and this is verified by the detailed calculations for k = 1. The behaviour for fixed t and q → 0 is shown to be markedly different from the Ornstein-Zernike approximation. Detailed comparison is provided with the scaling function of the t dependence of the correlations appearing in parallel work.