Abstract: | The two-point correlation function ? (q, ξ) is calculated in the critical region of momentum space q in terms of a suitable correlation lenght ξ, by means of perturbation expansion to order 1/n, for an n-vector system with long-range interactions decaying as , for , where a is the spacing on a d-dimensional lattice, σ < d < 2σ and 0 < σ ? 2 ? ηSR. The calculations are done in zero field for T ? Tc. Explicit expansions for long-range propagators are developed for and for the neighborhood of σ ? 2 ? ηSR, in terms of which a universal, cut-off independent scaling function is obtained over the whole range of , and it is shown that the amplitude of the correlation-length dependence of the susceptibility becomes a universal parameter. Both the exponents and the coefficients of the expansion for fixed q as are calculated explicitly. The former are shown to require the validity of the operator-product expansion and explicit logarithmic correction terms are obtained for . For these and other dimensionalities, the coefficients are shown to be finite functions of d and σ. The correction to the Ornstein-Zernike form is given explicitly, with non-integer powers of x that have finite coefficients. |