Scaling function for two-point correlations. I. Expansion near four dimensions

A detailed calculation to order ε² of the two-point correlation function in the zero-field critical region (T≥Tc) is presented for an n-vector system in d=4-ε dimensions. Scaling behavior is verified over the full parameter range and the scaling function is obtained as a universal explicit convergent integral (independent of any cutoffs). Study of the scaling function as T→Tc in the finite (q≠0) momentum limit, confirms the presence of terms varying as t^1-α and as t [with t=(T-Tc)Tc]; explicit evaluation of their amplitudes reliably determines the form of the scattering intensity at fixed q and locates the corresponding maximum accurately.