BETHE-PEIERLS-WEISS METHOD OF FERROMAGNETISM - ILLUSTRATIVE CALCULATION OF A PHASE-TRANSITION

The cluster method of ferromagnetism of Bethe, Peierls, and Weiss is studied for the case of spin S = 1/2 and simple cubic structure. A pedagogical calculation is made using the exact eigenfunctions and eigenvalues to compute the transition temperature (Tc), the short-range parameter, the energy per atom, the temperature dependence of the internal field, and the discontinuity in the specific heat at Tc. As it is well known from the original work of Weiss, short-range order effects are included in this theory yielding results above the Curie point which are not predicted by the molecular field theory but are present in most physical materials. On the other hand, the finite size of the cluster produces the instability of the ferromagnetic state at very low temperatures since the low-energy spin-wave states of long wavelength are not allowed. This appears to be the main limitation of the model which must be used cautiously in the ferromagnetic phase. © 1978, American Association of Physics Teachers. All rights reserved.