Phase transitions in the antiferromagnetic layered Ising model on a cubic lattice

Phase transitions of the layered antiferromagnetic Ising model on a cubic lattice with allowance for intralayer next nearest neighbor interactions in the range of $0.0\leqslant r <1.0$ have been studied on the basis of the replica algorithm by the Monte Carlo method. The character of phase transitions has been analyzed on the basis of the histogram method and the Binder cumulant method. The phase diagram of the dependence of the critical temperature on the next nearest neighbor interaction has been constructed. It has been shown that a secondorder phase transition is observed in the interval of $0.0\leqslant r\leqslant 0.5$ and for the value $r=0.9$ and a first-order phase transition is observed in the interval of $0.6\leqslant r< 0.8$.