Frustrated Ising model with competing interactions on a square lattice
Jae Hwan Lee, Seung‐Yeon Kim, Jin Min Kim
Abstract
The Ising model with nearest-neighbor and next-nearest-neighbor interactions of the coupling constants ${J}_{1}$ and ${J}_{2}$, respectively, is investigated on a square lattice. For ${J}_{1}=2$ and ${J}_{2}=1$, the model becomes frustrated because ground states are infinitely degenerate. We obtain the density of states by using the Wang-Landau Monte Carlo method and calculate the specific heat. We find two separate peaks in the specific heat: a sharp peak related to the critical behavior and a round peak related to the specific heat of a disordered system such as spin glass. As the system size increases, the sharp-peak temperature decreases towards zero, and the maximum height of the sharp peak increases logarithmically, supporting that the spatial correlation length diverges exponentially at zero temperature. The partition-function zeros calculated by the density of states also suggest the zero-temperature phase transition.