1ST-ORDER PHASE-TRANSITIONS IN THE ISING SQUARE LATTICE WITH 1ST-NEIGHBOR AND 2ND-NEIGHBOR INTERACTIONS

The phase diagram of the Ising square lattice with first- and second-n earest-neighbor antiferromagnetic interactions (J1 and J2) is calculat ed within the framework of the cluster-variation method. The Hamiltoni an is solved within the nine-point-cluster approximation. In contrast to previous studies we find that the phase transition from the superan tiferromagnetic to the paramagnetic state is of first order in the ran ge 0.5 < R = J1/J2 < 1.144. The non-Ising critical behavior observed i n that range of interactions might be due to that phenomenon.