Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat $\alpha$, susceptibility $\gamma$, order parameter $\beta$, and correlation radius $\nu$, as well as the Fisher index $\eta$, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.