Computer simulation of phase transitions of the Heisenberg antiferromagnetic model

Based on the replica algorithm by the Monte Carlo method, a computer simulation of the three-dimensional antiferromagnetic Heisenberg model is performed, taking into account the interactions of the first and second nearest neighbors. The phase transitions 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 $0.0 \leq r \leq 1.0$. The phase diagram of the critical temperature dependence on a value of the next-nearest neighbor interaction is plotted.