Second-Order Green's-Function Theory of the Heisenberg Ferromagnet

The coupled Green's-function equations for the Heisenberg ferromagnet are approximated by two coupled differential equations. The approximation agrees at low temperatures with Dyson's spin-wave theory. Computer solutions of spontaneous magnetization for spin ½ and a face-centered cubic lattice represent a better fit to the magnetization of nickel than that afforded by an earlier first-order theory. Compared with the latter, the parameter ${\theta }_c=\frac{k{T}_c}{J}$ for cubic lattices and for spin ½ is found to give closer agreement with values obtained from high-temperature series expansions. The renormalized exchange interaction, calculated for all temperatures below the Curie temperature, falls off with increasing temperature, and apparently represents a poorer fit to the experimental data than the results of the first-order theory.