Computer simulation of critical properties of the frustrated Ising model

Based on the replica algorithm by the Monte Carlo method, a computer simulation of the three-dimensional antiferromagnetic Ising model is performed, taking into account the interactions of the first and second nearest neighbors. The critical properties of this model are studied. The investigations were carried out for the ratios of the exchange interactions of the first and second nearest neighbors $r=J_2/J_1$ in the range $0.0 \leq r \leq 1.0$. In the framework of the theory of finite-dimensional scaling, all the main static critical exponents are calculated.