The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.
We have considered the
S=1∕2 antiferromagnetic Heisenberg model in two dimensions, with an additional Ising next-nearest-neighbor interaction. Antiferromagnetic next-nearest-neighbor interactions will lead to frustration, and the system responds with flipping the spins down in the
xy plane. For large next-nearest-neighbor coupling the system will order in a striped phase along the
z axis, this phase is reached through a first-order transition. We have considered two generalizations of this model, one with random next-nearest-neighbor interactions, and one with an enlarged unit cell, where only half of the atoms have next-nearest-neighbor interactions. In both cases the transition is softened to a second-order transition separating two ordered states. In the latter case we have estimated the quantum critical exponent $\ensuremath{\beta}\ensuremath{\approx}0.25$. These two cases then represent candidate examples of deconfined quantum criticality.