Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions

The critical properties of the antiferromagnetic layered Ising model on a cubic lattice with regard to the nearest-neighbor and next-nearest-neighbor interactions are investigated by the Monte Carlo method using the replica algorithm. The investigations are carried out for the ratios of exchange nearest-neighbor and next-nearest-neighbor interactions $r=J_{2}/J_{1}$ in the range of 0 $\le r\le$ 1.0. Using the finite-size scaling theory, the static critical indices of specific heat $\alpha$, order parameter $\beta$, susceptibility $\gamma$, correlation radius $\nu$, and Fisher index $\eta$ are calculated. It is shown that the universality class of the critical behavior of this model is retained in the range of 0 $\le r\le$ 0.4. It is established that the change in the next-nearest-neighbor interaction value in this model in the range of $r>$ 0.8 leads to the same universality class as the three-dimensional fully frustrated Ising model on the cubic lattice.