More Exact Results on a Binary Alloy with Next Nearest Neighbor Competing Interactions

Abstract

We study an Ising-type binary alloy with competing interactions between first and second neighbors on a Bethe lattice. Successive layers of the Bethe lattice are occupied in an alternating fashion by magnetic moments of type (A) and (B). We impose a restriction on the system by allowing only interlayer interactions between second neighbors. We approach the problem by setting up an iteration process for the partial partition functions. This correlates the partition function for a Bethe lattice with N layers to the partial partition functions of the Bethe lattice with N — 1 layers. The presence of competing interactions between first and second neighbors imposes frustration on these systems, which, in turn, enriches the resulting phase diagrams. We study the behavior of the system for varying degrees of competition between first and second neighbors. Besides the ferromagnetic (F) and paramagnetic (PM) phases, a modulated ferromagnetic phase (F') with periodicity two and an antiferromagnetic phase with periodicity four (AF-2) are present. The modulated phase (M) is present only for cases of very strong competition between first and second neighbor interactions. As the competition is reduced, the modulated phase (M) disappears. For weak competition, two new phases with periodicity four appear: In the first one, labeled (+++--), magnetic moments of one species align ferromagnetically, while those of the other species align antiferromagnetically. In the second phase, (++++), both species align in a ferromagnetic fashion.