Correlation functions for anisotropic heisenberg model in zero magnetic field

Analysis of the exact solution of the Ising model for a linear chain provides the basis for a scheme of systematic calculation of the correlation functions of arbitrary order for a system of spins coupled by the exchange interaction at temperatures above the critical point. The correlation functions can be calculated from the equation of long-range coupling that is derived; it has the form $\langle S_f^\alpha A\rangle=\eta_\alpha\langle\sigma_f^\alpha A\rangle$, where $\displaystyle\sigma_f^\alpha=\sum_{f'}A_{ff'}^\alpha S_{f'}^\alpha$ is the operator of the local field, $\eta_\alpha$ are the temperature parameters of the model, and $A_{ff'}^\alpha$ is the interaction potential, $\alpha=x,y,z$. A comparison is made with the exact solutions for the one- and two-dimensional Ising models.