First-order phase transitions in the Ising square lattice with first- and second-neighbor interactions

Abstract

The phase diagram of the Ising square lattice with first- and second-nearest-neighbor antiferromagnetic interactions (${\mathit{J}}_{1}$ and ${\mathit{J}}_{2}$) is calculated within the framework of the cluster-variation method. The Hamiltonian is solved within the nine-point-cluster approximation. In contrast to previous studies we find that the phase transition from the superantiferromagnetic to the paramagnetic state is of first order in the range 0.5R=${\mathit{J}}_{1}$/${\mathit{J}}_{2}$1.144. The non-Ising critical behavior observed in that range of interactions might be due to that phenomenon.