Calculation of a pair correlation function for the three-dimensional Ising model with long-range exchange forces

A simple difference equation for one type of correlators has been obtained by the method of direct calculation of the correlation functions (CF). It is correct for the Ising model of an arbitrary dimension with the exactness O(1z) (z-number of particles covered by the interaction potential). The equation obtained is used to calculate the pair CF 〈SzfSzj〉 in the three-dimensional Ising model with long-range forces which are of importance when dealing with the applied magnetic problems. The results of the calculations lead to corrections in the Ornstein-Zernike (OZ) theory.