Frustrated Ising model with competing interactions on a square lattice

The Ising model with nearest-neighbor and next-nearest-neighbor interactions of the coupling constants J₁ and J₂, respectively, is investigated on a square lattice. For J₁=2 and J₂=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.