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

초록

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 0 <= R < 1/2 and J(2) < 0 (Ising antiferromagnet). For R > 1/2 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.

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