Spherical Model of an Antiferromagnet
Abstract
The sphericalization technique is adapted to the calculation of the partition function of a bodycentered cubic lattice of spins with isotropic antiferromagnetic interactions between nearest neighbors and between secondnearest 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 secondnearest neighbor interaction to the nearestneighbor interaction. In addition a firstorder 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 longrange order is measured in terms of longrange 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 longrange order. In contrast to the molecular field theory, this model should give valid predictions for quantities depending on shortrange order.
 Publication:

Physical Review
 Pub Date:
 August 1954
 DOI:
 10.1103/PhysRev.95.676
 Bibcode:
 1954PhRv...95..676G