Phase diagram of the antiferromagnetic Heisenberg model on a cubic lattice

Phase transitions in the antiferromagnetic Heisenberg model on a cubic lattice with intralayer next-nearest neighbor interactions are studied using the replica Monte Carlo algorithm. The magnitude of next-nearest neighbor interactions varies in the range of $0.0 \leqslant r\leqslant 1.0$. The characteristics of the phase transitions are analyzed by the histogram and Binder cumulant techniques. The phase diagram relating the transition temperature and the magnitude of next-nearest neighbor interactions is constructed. It is shown that a second order phase transition occurs in the $r$ range under study. In this model, it is found that the intralayer next-nearest neighbor interactions do not change the order of the phase transition.