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

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.

Uncovering the secrets of the 2D random-bond Blume–Capel model

“…These predictions have been confirmed by various Monte Carlo simulations and they have been also well verified by our recent numerical studies via a two-stage WL method [ 5,6,7]. The random-bond version of the BC model is defined by the Hamiltonian…”

“…We now consider the critical behavior at ∆ = 1.975 [ 7]. Figure 3 is well obeyed for several pure and disordered models, including the pure and randombond version of the square Ising model with nearest-and next-nearest-neighbor competing interactions [ 6]. At ∆ = 1 the random version should be comparable with the random Ising model, a model that has been extensively investigated and debated [ 6,14,15,16,17,18,19,20].…”

Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bondd=2Blume-Capel model

“…Pure systems with a zero specific heat exponent (α = 0) are marginal cases of Harris criterion (since the criterion does not give any information) and their study, upon the introduction of disorder, has been of particular interest. The paradigmatic model of the marginal case is, of course, the general random 2d Ising model (random-site, random-bond, and bond-diluted) and this model has been extensively investigated and debated [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Several recent studies, both analytical (renormalization group and conformal field theories) and numerical (mainly Monte Carlo (MC) simulations) devoted to this model, have provided very strong evidence in favor of the so-called logarithmic corrections's scenario.…”

Corrections to scaling in the dynamic approach to the phase transition with quenched disorder

“…In the inset of Fig. 3, a single peak structure for the random-bond Potts model at r = 10 is clearly observed, which is a standard signal of a second-order phase transition [21,24].…”

“…If α p < 0 or ν p > 2/d, the disorder is irrelevant to the critical behavior, and if α p > 0 or ν p < 2/d, the disorder is relevant, and leads to a new universality class governed by the 'disorder' fixed point [7,11]. For the marginal case α p = 0, the criterion can not give a conclusion whether the disorder is relevant or not, and numerical results support that the model obeys the strong universality hypothesis with logarithmic correlations [5,24]. On the other hand, for a disordered system with a continuous phase transition, which is governed by the 'disorder' fixed point, the specific heat exponent α does not decide whether the disorder is relevant.…”