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

Abstract

We study the square-lattice Ising model with nearest-neighbor ( J 1 ) and next nearest-neighbor ( J 2 ) interactions, using the Wang–Landau Monte Carlo algorithm and the partition function zeros in the complex temperature plane (Fisher zeros). Here, the competition between J 1 and J 2 interactions is defined by the coupling ratio R = J 2 / J 1 . For J 2 > 0, the critical behavior is trivial and is the same as the square-lattice Ising model with only J 1 interaction. On the other hand, the new phase of superantiferromagnet appears for J 2 < 0. However, the nature of the transition into the superantiferromagnetic phase is still controversial in the literature. To resolve the controversy, we estimate the critical temperature T c ( R ) and thermal scaling exponent y t ( R ) from the Fisher zeros, as a function of R . The estimated values of T c ( R ) agree well with the results in the literature. We obtain the simple critical behavior with a fixed value of the thermal scaling exponent, y t ( R ) = 1, for and J 2 < 0 (Ising antiferromagnet). For and J 2 < 0 (Ising superantiferromagnet), however, it is shown that y t ( R ) continuously varies depending on R values, and the estimated values of y t ( R ) are clearly less than that of the first-order phase transition, y t = 2.