Method of functional integration in the theory of spin systems

A convenient functional integral representation is proposed for the free energy and Green's function of the generalized quantum Heisenberg model. The representation can be used in the investigation of a large class of problems. A simple functional integration gives the results of the random phase approximation in the lowest approximation. Explicit expressions are given for the free energy of some model spin systems. The higher fluctuation corrections are taken into account by means of an expansion with respect to Gaussian moments with renormalized interaction.