A Theory of Antiferromagnetism

TLDR: In this paper, the Bethe-based method is used to calculate the density matrix of a duster exactly without the perturbation method, and it is shown that the magnetization of the sublattice is completely saturated at OOK in just the same way as in the Ising model.

Abstract: based on Heisenberg model is developed by a method which is much more directly the analogue of the original B~the method than Weiss-Li's. By the present method, the calculations can be carried out over all temperatures. Especially, the situation at lower temperatures which is obscure in Weiss·U's papers is made dear. Thus we can see that an anti·Curie point which Anderson has proposed, does not occur, if we calculate the density matrix of a duster exactly without the perturbation method. By considering only a small cluster, being characteristic of the Bethe approxi· mation, the long wavelength spin waves, which are important at lower temperatures, are excluded, so that the magnetization of the sublattice is completely saturated at OOK in just the same way as in the Ising model. It is shown that, in the Bethe approximation, Curie point of antiferromagnet is higher than that of ferromagnet, for the same magnitude of I J I·.