Phase transitions in a frustrated Ising antiferromagnet on a square lattice

The phase transitions occurring in the frustrated Ising square antiferromagnet with first- ($J_1<0$) and second- ($J_2<0$) nearest-neighbor interactions are studied within the framework of the effective-field theory with correlations based on the different cluster sizes and for a wide range of $R=J_2\mathrm{/}\mathrm{\mid }{J}_1\mathrm{\mid }$. Despite the simplicity of the model, it has proved difficult to precisely determine the order of the phase transitions. In contrast to the previous effective-field study, we have found a first-order transition line in the region close to $R=-0.5$ not only between the superantiferromagnetic and paramagnetic ($R<-0.5$) but also between antiferromagnetic and paramagnetic ($R>-0.5$) phases.