Ising Model with Antiferromagnetic Next-Nearest-Neighbor Coupling. II. Ground States and Phase Diagrams

Abstract

The critical values of the ratio of interaction energies at which the ordering of spins in the ground state is indeterminate (and probably $T_c=0\mathrm{}$) are calculated exactly for a variety of Ising lattices with antiferromagnetic next-nearest-neighbor coupling, and for anisotropic nearest-neighbor coupling. Using these results and the exact two-dimensional solutions, the general dependence of the critical point on interaction ratio is sketched. The complex case of the antiferromagnetic fcc is reconsidered.