Low-temperature expansion of spin Green's functions and Dyson–Maleev formalism

A one-toLone correspondence is established in general form between the calculation of the spin Green's functions in the Maleev representation and their calculation in the technique of spin operators. It is shown that the non-Hermiticity of the Maleev representation does not affect the results of the calculations, and the contribution of the unphysical states in the case of a Heisenberg ferromagnet for $T<SJ_0$ is exponentially small – of order $\exp(-T^\ast/T)$, where $T^\ast=S(2S+1)J_0$ ($S$ is the spin of the atom, and $J_0$ is the Fourier component of the exchange integral with zero wave vector).