Spherical Model of an Antiferromagnet
Barry S. Gourary, Robert Weisbein Hart · Physical Review · 1954
The sphericalization technique is adapted to the calculation of the partition function of a body-centered cubic lattice of spins with isotropic antiferromagnetic interactions between nearest neighbors and between second-nearest neighbors. Two transition points may be obtained. The usual Curie point transition from the paramagnetic state to the antiferromagnetic state (caused by the sticking of the saddle point) leads to an antiferromagnetic state with ordering either of the first kind or of the second kind, depending on the value of the ratio of the second-nearest neighbor interaction to the nearest-neighbor interaction. In addition a first-order transition from one kind of ordering to the other can occur if the ratio of the interactions varies with the specific volume in such a way that it moves through a critical value. Mathematically, this transition occurs because the largest eigenvalue of the interaction matrix becomes triply degenerate at the temperature at which the ratio of the interactions attains the critical value.The long-range order is measured in terms of long-range order parameters, which are closely related to the sublattice magnetizations. The analog of the perpendicular susceptibility is also calculated.Qualitative agreement with the molecular field theory is obtained for all those properties of the model which depend on the long-range order. In contrast to the molecular field theory, this model should give valid predictions for quantities depending on short-range order.