MODIFIED FUNCTIONAL INTEGRAL METHOD FOR THE HEISENBERG-MODEL

We propose a modified functional integral method for the S=1/2 three d imensional ferromagnetic Heisenberg model based on the Popov and Fedot ov theory. The correlation functions expressed by the auxiliary fields are required to satisfy the spin commutation and anticommutation rela tions. In one-loop approximation for the partition function, obtained results are in exact agreement with the Tyablikov result of the Green function method of the Heisenberg ferromagnet. This result provides a possible explanation of the physical meaning of the Tyablikov decoupli ng approximation. Furthermore introducing a higher order correction in to the unperturbed part of the partition function, we improve the appr oximation and we obtain thermal quantities. At low temperatures the te mperature dependence of the spin-wave energy is in exact agreement wit h that of Dyson. Compared with Callen's result, for the temperature de pendence of the spontaneous magnetization our result is closer to that of Dyson. The Curie temperature and the critical indices agree with t hose of the molecular field theory of the Heisenberg ferromagnet.