Modified Callen decoupling in the Green's-function theory of Heisenberg antiferromagnets

Abstract

The modified Callen decoupling (MCD) is extended to Heisenberg antiferromagnets with exchange between more than nearest neighbors. The results are illustrated by application to type-I order in the three cubic lattices. It is shown that type-I order in simple cubic and body-centered-cubic lattices is especially simple---and therefore especially stable---due to several accidental symmetries. The more general case is typified by type-I order in a face-centered-cubic lattice, which shows an instability at intermediate temperatures for all values of the exchange constants when $S=\frac{1}{2}$. The MCD results are compared to the Pad\'e-approximant estimates of the N\'eel temperatures and are shown to explain the anomalous behavior found for spin \textonehalf{}.