We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor ( J nn ) and next-nearest-neighbor ( J nnn ) antiferromagnetic interactions. We consider the case R = J nn / J nnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.
We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor ( J nn ) and next-nearest-neighbor ( J nnn ) antiferromagnetic interactions. We consider the case R = J nn / J nnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.
Abstract. We investigate and contrast, via entropic sampling based on the Wang-Landau algorithm, the effects of quenched bond randomness on the critical behavior of two Ising spin models in 2D. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple Ising model are studied and their general universality aspects are inspected by a detailed finite-size scaling (FSS) analysis. We find that, the random bond SAF model obeys weak universality, hyperscaling, and exhibits a strong saturating behavior of the specific heat due to the competing nature of interactions. On the other hand, for the random Ising model we encounter some difficulties for a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. Yet, a careful FSS analysis of our data favors the field-theoretically predicted logarithmic corrections.
We investigate and contrast, via entropic sampling based on the Wang–Landau algorithm, the effects of quenched bond randomness on the critical behavior of two Ising spin models in 2D. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple Ising model are studied, and their general universality aspects are inspected by means of a detailed finite size scaling (FSS) analysis. We find that the random bond SAF model obeys weak universality, hyperscaling, and exhibits a strong saturating behavior of the specific heat due to the competing nature of interactions. On the other hand, for the random Ising model we encounter some difficulties as regards a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. However, a careful FSS analysis of our data favors the field theoretically predicted logarithmic corrections.
We investigate and contrast, via the Wang-Landau (WL) algorithm, the effects of quenched bond randomness on the self-averaging properties of two Ising spin models in 2d. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple ferromagnetic Ising model are studied. We find that, the random bond SAF model shows a strong violation of self-averaging, much stronger than that observed in the case of the random bond Ising model. Our analysis of the asymptotic scaling behavior of the variance of the distribution of the sample-dependent pseudocritical temperatures is found to be consistent with the renormalization group prediction of Aharony and Harris. Using this alternative approach, we find estimates of the correlation length exponent ν in agreement with results obtained from the usual finite-size scaling (FSS) methodology.
We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the two-dimensional Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with nu=1.30(6) and beta/nu = 0.128(5) . These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems with and without quenched disorder. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.
We study, via a two-stage Wang–Landau (WL) strategy, the random-bond version of the square lattice ferromagnetic Blume–Capel (BC) model, in both the first- and second-order phase transition regimes of the pure model. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with v=1.30(6) and β/v=0.128(5). These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of 2d systems with and without quenched disorder.
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.