Universality aspects of the d=3 random-bond Blume-Capel model

The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-order regime of the pure model, belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site- and bond-dilution). The second, amounts to a strong violation of universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.

Quenched bond randomness in marginal and non-marginal Ising spin models in 2D

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.

Self-averaging and criticality: A comparative study in 2d random bond spin models

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 $ u$ in agreement with results obtained from the usual finite-size scaling (FSS) methodology.

First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions

We implement a new and accurate numerical entropic scheme to investigate the first-order transition features of the triangular Ising model with nearest-neighbor ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic interactions in ratio $R=J_{nn}/J_{nnn}=1$. Important aspects of the existing theories of first-order transitions are briefly reviewed, tested on this model, and compared with previous work on the Potts model. Using lattices with linear sizes $L=30,40,...,100,120,140,160,200,240,360$ and 480 we estimate the thermal characteristics of the present weak first-order transition. Our results improve the original estimates of Rastelli et al. and verify all the generally accepted predictions of the finite-size scaling theory of first-order transitions, including transition point shifts, thermal, and magnetic anomalies. However, two of our findings are not compatible with current phenomenological expectations. The behavior of transition points, derived from the number-of-phases parameter, is not in accordance with the theoretically conjectured exponentially small shift behavior and the well-known double Gaussian approximation does not correctly describe higher correction terms of the energy cumulants. It is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections.

Wang-Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions

We report results of a Wang-Landau study of the random bond square Ising model with nearest- ($J_{nn}$) 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 $alpha$. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length $ u$, magnetization $beta$, and magnetic susceptibility $gamma$ increase when compared to the pure model, the ratios $beta/ u$ and $gamma/ u$ 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.

First-order transition features of the 3D bimodal random-field Ising model

Two numerical strategies based on the Wang-Landau and Lee entropic sampling schemes are implemented to investigate the first-order transition features of the 3D bimodal ($pm h$) random-field Ising model at the strong disorder regime. We consider simple cubic lattices with linear sizes in the range $L=4-32$ and simulate the system for two values of the disorder strength: $h=2$ and $h=2.25$. The nature of the transition is elucidated by applying the Lee-Kosterlitz free-energy barrier method. Our results indicate that, despite the strong first-order-like characteristics, the transition remains continuous, in disagreement with the early mean-field theory prediction of a tricritical point at high values of the random-field.