Wang-Landau study of the 3D Ising model with bond disorder

We implement a two-stage approach of the Wang-Landau algorithm to investigate the critical properties of the 3D Ising model with quenched bond randomness. In particular, we consider the case where disorder couples to the nearest-neighbor ferromagnetic interaction, in terms of a bimodal distribution of strong versus weak bonds. Our simulations are carried out for large ensembles of disorder realizations and lattices with linear sizes $L$ in the range $L=8-64$. We apply well-established finite-size scaling techniques and concepts from the scaling theory of disordered systems to describe the nature of the phase transition of the disordered model, departing gradually from the fixed point of the pure system. Our analysis (based on the determination of the critical exponents) shows that the 3D random-bond Ising model belongs to the same universality class with the site- and bond-dilution models, providing a single universality class for the 3D Ising model with these three types of quenched uncorrelated disorder.Comment: 7 pages, 7 figures, to be published in Eur. Phys. J.

Critical aspects of three-dimensional anisotropic spin-glass models

We study the $\pm J$ three-dimensional Ising model with a longitudinal anisotropic bond randomness on the simple cubic lattice. The random exchange interaction is applied only in the $z$ direction, whereas in the other two directions, $xy$ - planes, we consider ferromagnetic exchange. By implementing an effective parallel tempering scheme, we outline the phase diagram of the model and compare it to the corresponding isotropic one, as well as to a previously studied anisotropic (transverse) case. We present a detailed finite-size scaling analysis of the ferromagnetic - paramagnetic and spin glass - paramagnetic transition lines, and we also discuss the ferromagnetic - spin glass transition regime. We conclude that the present model shares the same universality classes with the isotropic model, but at the symmetric point has a considerably higher transition temperature from the spin-glass state to the paramagnetic phase. Our data for the ferromagnetic - spin glass transition line are supporting a forward behavior in contrast to the reentrant behavior of the isotropic model.Comment: 10 pages, 9 eps figures, 1 table, corrected symbolis

Critical aspects of the random-field Ising model

We investigate the critical behavior of the three-dimensional random-field Ising model (RFIM) with a Gaussian field distribution at zero temperature. By implementing a computational approach that maps the ground-state of the RFIM to the maximum-flow optimization problem of a network, we simulate large ensembles of disorder realizations of the model for a broad range of values of the disorder strength h and system sizes  = L3, with L ≤ 156. Our averaging procedure outcomes previous studies of the model, increasing the sampling of ground states by a factor of 103. Using well-established finite-size scaling schemes, the fourth-order’s Binder cumulant, and the sample-to-sample fluctuations of various thermodynamic quantities, we provide high-accuracy estimates for the critical field hc, as well as the critical exponents ν, β/ν, and γ̅/ν of the correlation length, order parameter, and disconnected susceptibility, respectively. Moreover, using properly defined noise to signal ratios, we depict the variation of the self-averaging property of the model, by crossing the phase boundary into the ordered phase. Finally, we discuss the controversial issue of the specific heat based on a scaling analysis of the bond energy, providing evidence that its critical exponent α ≈ 0−

Random-field Ising model: Insight from zero-temperature simulations

We enlighten some critical aspects of the three-dimensional ($d=3$) random-field Ising model from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian random-field Ising model and an equal-weight trimodal random-field Ising model. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and systems sizes $\mathcal{V}=L\times L\times L$, where $L$ denotes linear lattice size and $L_{\rm max}=156$. Using as finite-size measures the sample-to-sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field $h_{\rm c}$ and the critical exponent $\nu$ of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian random-field Ising model at the best-known value of the critical field provide the magnetic exponent ratio $\beta/\nu$ with high accuracy and clear out the controversial issue of the critical exponent $\alpha$ of the specific heat. Finally, we discuss the infinite-limit size extrapolation of energy- and order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.Comment: 14 pages, 8 figure

Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality's hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected d = 3 Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg

Fluctuations and criticality in the random-field Ising model

We investigate the critical properties of the d=3 random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength h and system sizes V=L×L×L, with L≤156. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength hc and the correlation length exponent ν. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent α and the violation of the hyperscaling exponent θ. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios β/ν and γ̄/ν, respectively. © 2013 American Physical Society

Analysis of the cluster formation in two-component cylindrical bottle-brush polymers under poor solvent conditions. A simulation study

Two-component bottle-brush polymers, where flexible side chains containing N = 20, 35 and 50 effective monomers are grafted alternatingly to a rigid backbone, are studied by Molecular Dynamics simulations, varying the grafting density $\sigma$ and the solvent quality. Whereas for poor solvents and large enough $\sigma$ the molecular brush is a cylindrical object with monomers of different type occupying locally the two different halves of the cylinder, for intermediate values of $\sigma$ an axially inhomogeneous structure of “pearl-necklace” type is formed, where microphase separation between monomers of different type within a cluster takes place. These “pearls” have a strongly non-spherical ellipsoidal shape, due to the fact that several side chains cluster together in one “pearl”. We discuss the resulting structures in detail and we present a comparison with the single-component bottle-brush case

Universality from disorder in the random-bond Blume-Capel model

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L∗≈32 for the chosen parameters. © 2018 American Physical Society