Method of variational derivatives in the theory of spin waves at low temperatures

Method of variational derivatives is applied to investigation of the low temperature properties of the isotropic Heisenberg ferromagnet with $S=1/2$. Expressions for the Green functions which include the Hartree–Fock terms and take into account the magnon scattering from the magnetization fluctuations and from each other are shown to give the correct description of the temperature dependence of the magnetization and of the magnon frequency.