Critical properties in the Ising model on a triangular lattice with the variable interlayer exchange interaction

Phase transitions and critical and thermodynamic properties of the three-dimensional antiferromagnetic Ising model on a layered triangular lattice with variable interlayer exchange interaction are studied by the replica algorithm of the Monte Carlo method. The studies are carried out for the ratios of the intralayer $J_1$ and interlayer $J_2$ exchange interactions in the range of $r=J_{2}/J_{1}$ = 0.01–1.0. It is established that a second-order phase transition is observed in the considered $r$ interval. Using the finite size scaling theory, the static critical exponents of the heat capacity $\alpha$, susceptibility $\gamma$, order parameter $\beta$, correlation radius $\nu$, and Fisher index $\eta$ are calculated. It is shown that the universality class of the critical behavior of this model is preserved in the interval of 0.05 $< r\le$ 1.0. It was found that with a further decrease in the $r$ value, a crossover from the three-dimensional critical behavior to the quasi-two-dimensional one is observed.