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 and having a term in equal to that found by Dyson in first Born approximation; terms arising from the approximations of the theory first appear in order , so that a spurious term does appear for , 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 . 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.
- Received 26 December 1962
DOI:https://doi.org/10.1103/PhysRev.130.890
©1963 American Physical Society