Magnons at the Curie temperature

Random phase approximations (RPA) have very successfully treated spin wave excitations in Heisenberg ferromagnets at low temperatures. The role played by these magnons at the order-disorder transition, however, has been a topic which has eluded RPA theories to date. In light of recent data1, the idea of magnons at the Curie temperature and above has become more difficult to refute. This adds incentive to attempt to model interacting magnons at the Curie temperature. This work examines some attempts to formulate higher random phase approximations and discusses why they fail as they approach the transition temperature. A new interpretation of some work by Parmenter and author2 is presented. The nature of the approximations made in that work is discussed, and an attempt is made to eliminate incorrect contributions from the energetically disfavored paramagnetic state to the correct magnon renormalization. A solution is presented which has the proper low temperature behavior as demonstrated by Dyson3 restored and the reentrant behavior eliminated. An examination of how close this model comes to behaving correctly is performed, and a comparison is made to some recent work by Parmenter4