A study of the critical properties of the Ising model on body-centered cubic lattice taking into account the interaction of next behind nearest neighbors

The replica Monte Carlo method has been used to investigate the critical behavior of a threedimensional antiferromagnetic Ising model on a body-centered cubic lattice, taking into account interactions of the adjacent behind neighbors. Investigations are carried out for the ratios of the values of exchange interactions behind the nearest and next nearest neighbors $k=J_2/J_1$ in the range of $k\in$ [0.0, 1.0] with the step $\Delta k$ = 0.1. In the framework of the theory of finite-dimensional scaling the static critical indices of heat capacity $\alpha$, susceptibility $\gamma$, of the order parameter $\beta$, correlation radius $\nu$, and also the Fisher index $\eta$ are calculated. It is shown that the universality class of the critical behavior of this model is kept in the interval of $k\in$ [0.0, 0.6]. It is established that a nonuniversal critical behavior is observed in the range $k\in$ [0.8, 1.0].