Study of a square-lattice Ising superantiferromagnet using the Wang–Landau algorithmand partition function zeros

Abstract

We study the square-lattice Ising model with nearest-neighbor (J1) and nextnearest-neighbor (J2) interactions, using the Wang–Landau Monte Carlo algorithm and the partition functionzeros in the complex temperature plane (Fisher zeros). Here, the competition betweenJ1 andJ2 interactions is definedby the coupling ratio R = J2/J1. For J2 > 0, the critical behavior is trivial and is the same as the square-lattice Ising model with onlyJ1 interaction. On the other hand, the new phase of superantiferromagnet appears forJ2 < 0. However, the nature of the transition into the superantiferromagnetic phase is stillcontroversial in the literature. To resolve the controversy, we estimate the critical temperatureTc(R) and thermal scalingexponent yt(R) from the Fisherzeros, as a function of R.The estimated values of Tc(R) agree well with the results in the literature. We obtain the simplecritical behavior with a fixed value of the thermal scaling exponent,yt(R) = 1, for and J2 < 0 (Ising antiferromagnet). For and J2 < 0 (Ising superantiferromagnet), however, it is shown thatyt(R) continuously variesdepending on R values, andthe estimated values of yt(R) are clearly less than that of the first-order phase transition,yt = 2.