Use of Green Functions in the Theory of Ferromagnetism. II. Dyson Spin Waves

We treat Dyson's ideal-spin-wave Hamiltonian by Green's function methods. In the second section we consider only noninteracting Dyson spin waves. In the third section we consider interacting spin waves, using the simplest possible decoupling assumption. Our results lead then to the same expressions for the magnetization and the spin-wave specific heats as Dyson in the limit as $S\to \infty$ up to terms of order $T^4$. The difference is of order $\frac{T^4}{S^2}$. If we introduce a higher-order decoupling, we obtain results identical with those of Oguchi, which in turn agree fairly closely with those of Dyson. We also obtain a spin-wave dispersion law which is a slight improvement of the one obtained by Brout and Englert, especially for small values of $S$. In three appendices we discuss, respectively, the decoupling process, the shifts in the spin-wave energies, and their "damping."