Higher-order approximations for dynamical spin correlation functions in high-temperature paramagnets

A method of generating equations for dynamical two-point spin correlation functions for systems interacting via spin-spin interactions in the high-temperature limit is presented. The method is exact in the sense that all moments of the correlation functions are exact to order $\frac{1}{Z}$ where $Z$ is the effective number of nearest spin neighbors. Thus the equations are formally exact in the limit of large dimensionality with nearest-neighbor interactions. As an example the method is applied to the isotropic Heisenberg paramagnet.