Green Function Theory of Ferromagnetism

Abstract

A theory of ferromagnetism for general spin, approximately valid through the entire temperature range, is given. At low temperatures the magnetization agrees with the Dyson results, having no term in $T^3$ and having a term in $T^4$ equal to that found by Dyson in first Born approximation; terms arising from the approximations of the theory first appear in order $T^{\frac{3(2S+1)\mathrm{}}{2}}$, so that a spurious $T^3$ term does appear for $S=\frac{1}{2}$, but for no other spin. Curie temperatures are within a few percent of the Brown and Luttinger estimates for spins greater than unity, and agree within 1% of the Domb and Sykes estimate of the large-spin limit. The susceptibility at high temperatures agrees with the Opechowski expansion to terms in $\frac{1}{T^2}$. The quasiparticle energies are renormalized by the energy at low temperature and by the magnetization at higher temperature. The Green function is decoupled by a physical criterion involving self-consistency of the decoupling at all temperatures. The Green function method is extended to higher spin by a technique of parametrizing the Green function and explicitly finding the functional dependence on this parameter by solution of an auxiliary differential equation.