CVM modeling of the square Ising lattice with one next-nearest-neighbor interaction

As an analysis of the development of first-order behavior in two-dimensional Ising lattices, the square lattice with antiferromagnetic nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction in the (11) direction has been modeled. The phase diagram was calculated for a range of interaction parameters and imposed fields; the calculations were performed using the cluster variation method (CVM). Analysis of the calculations suggests that no first-order behavior is developed in this system, so that higher dimensionality or connectivities are required before such behavior is developed.