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

Critical dynamics of cluster algorithms in the random-bond Ising model

In the present work, we present an extensive Monte Carlo simulation study on the dynamical properties of the two-dimensional random-bond Ising model. The correlation time τ of the Swendsen-Wang and Wolff cluster algorithms is calculated at the critical point. The dynamic critical exponent z of both algorithms is also measured by using the numerical data for several lattice sizes up to L=512. It is found for both algorithms that the autocorrelation time decreases considerably and the critical slowing-down effect reduces upon the introduction of bond disorder. Additionally, simulations with the Metropolis algorithm are performed, and the critical slowing-down effect is observed to be more pronounced in the presence of disorder, confirming the previous findings in the literature. Moreover, the existence of the non-self-averaging property of the model is demonstrated by calculating the scaled form of the standard deviation of autocorrelation times. Finally, the critical exponent ratio of the magnetic susceptibility is estimated by using the average cluster size of the Wolff algorithm.

Two-dimensional dilute Baxter-Wu model: Transition order and universality

We investigate the critical behavior of the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal-field coupling Δ with the goal of determining the universality class of transitions along the second-order part of the transition line as one approaches the putative location of the multicritical point. We employ extensive Monte Carlo simulations using two different methodologies: (i) a study of the zeros of the energy probability distribution, closely related to the Fisher zeros of the partition function, and (ii) the well-established multicanonical approach employed to study the probability distribution of the crystal-field energy. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram supports previous claims that the transition belongs to the universality class of the four-state Potts model. For positive values of Δ, we observe the presence of strong finite-size effects, indicative of crossover effects due to the proximity of the first-order part of the transition line. Finally, we demonstrate how a combination of cluster and heat-bath updates allows one to equilibrate larger systems, and we demonstrate the potential of this approach for resolving the ambiguities observed in the regime of Δ≳0.

Antiferromagnetic Blume-Capel model of the disordered Fe-Mn-Al ternary system

The magnetic properties and thermodynamical description of the Fe-Mn-Al ternary alloy are studied using the spin 1 antiferromagnetic Blume-Capel (BC) model by the pair approximation based on the Gibbs-Feymann-Bogoliubov inequality for the free energy. The values of the spin operator are +1 for ferromagnetic interaction (Fe-Fe), -1 for the antiferromagnetic one (Mn-Mn, Mn-Fe), and 0 for the magnetic diluter (corresponding to Al). The BC model with antiferromagnetic (AF) next-nearest-neighbor coupling better accurately fit the mean hyperfine field experimental data obtained by Mössbauer spectroscopy. Considering the crystalline field, the predicted temperature as a function of the Al concentration phase diagram, for the fcc lattice, from the numerical solution is remarkably good and significantly improves the traditional Ising and random-site Ising models.

Universality in the two-dimensional dilute Baxter-Wu model

We study the question of universality in the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal field Δ. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of Δ and a parallelized variant of the multicanonical approach performed at constant temperature T. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram indicates that the transition belongs to the universality class of the four-state Potts model. Previous controversies with respect to the nature of the transition are discussed and attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model.

Metastable behavior of the spin-s Ising and Blume-Capel ferromagnets: A Monte Carlo study

We present an extensive Monte Carlo investigation of the metastable lifetime through the reversal of the magnetization of spin-s Ising and Blume-Capel models, where s={1/2,1,3/2,2,5/2,3,7/2}. The mean metastable lifetime (or reversal time) is studied as a function of the applied magnetic field, and for both models it is found to obey the Becker-Döring theory, as was initially developed for the case of an s=1/2 Ising ferromagnet within the classical nucleation theory. Moreover, the decay of the metastable volume fraction nicely follows Avrami's law for all values of s and for both models considered.

Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

Using high-precision Monte Carlo simulations based on a parallel version of the Wang-Landau algorithm and finite-size scaling techniques, we study the effect of quenched disorder in the crystal-field coupling of the Blume-Capel model on a square lattice. We mainly focus on the part of the phase diagram where the pure model undergoes a continuous transition, known to fall into the universality class of a pure Ising ferromagnet. A dedicated scaling analysis reveals concrete evidence in favor of the strong universality hypothesis with the presence of additional logarithmic corrections in the scaling of the specific heat. Our results are in agreement with an early real-space renormalization-group study of the model as well as a very recent numerical work where quenched randomness was introduced in the energy exchange coupling. Finally, by properly fine tuning the control parameters of the randomness distribution we also qualitatively investigate the part of the phase diagram where the pure model undergoes a first-order phase transition. For this region, preliminary evidence indicate a smoothing of the transition to second-order with the presence of strong scaling corrections.

Frustrated Potts model: Multiplicity eliminates chaos via reentrance

The frustrated q-state Potts model is solved exactly on a hierarchical lattice, yielding chaos under rescaling, namely, the signature of a spin-glass phase, as previously seen for the Ising (q=2) model. However, the ground-state entropy introduced by the (q>2)-state antiferromagnetic Potts bond induces an escape from chaos as multiplicity q increases. The frustration versus multiplicity phase diagram has a reentrant (as a function of frustration) chaotic phase.

Deep learning on the 2-dimensional Ising model to extract the crossover region with a variational autoencoder

The 2-dimensional Ising model on a square lattice is investigated with a variational autoencoder in the non-vanishing field case for the purpose of extracting the crossover region between the ferromagnetic and paramagnetic phases. The encoded latent variable space is found to provide suitable metrics for tracking the order and disorder in the Ising configurations that extends to the extraction of a crossover region in a way that is consistent with expectations. The extracted results achieve an exceptional prediction for the critical point as well as agreement with previously published results on the configurational magnetizations of the model. The performance of this method provides encouragement for the use of machine learning to extract meaningful structural information from complex physical systems where little a priori data is available.

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

We obtain the phase diagram for the Blume-Capel model with the bimodal distribution for random crystal fields, in the space of three fields: temperature (T), crystal field (Δ), and magnetic field (H) on a fully connected graph. We find three different topologies for the phase diagram, depending on the strength of disorder. Three critical lines meet at a tricritical point only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first-order surface in the H=0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.

Monte Carlo study of the interfacial adsorption of the Blume-Capel model

We investigate the scaling of the interfacial adsorption of the two-dimensional Blume-Capel model using Monte Carlo simulations. In particular, we study the finite-size scaling behavior of the interfacial adsorption of the pure model at both its first- and second-order transition regimes, as well as at the vicinity of the tricritical point. Our analysis benefits from the currently existing quite accurate estimates of the relevant (tri)critical-point locations. In all studied cases, the numerical results verify to a level of high accuracy the expected scenarios derived from analytic free-energy scaling arguments. We also investigate the size dependence of the interfacial adsorption under the presence of quenched bond randomness at the originally first-order transition regime (disorder-induced continuous transition) and the relevant self-averaging properties of the system. For this ex-first-order regime, where strong transient effects are shown to be present, our findings support the scenario of a non-divergent scaling, similar to that found in the original second-order transition regime of the pure model.

Dynamic phase transitions in the presence of quenched randomness

We present an extensive study of the effects of quenched disorder on the dynamic phase transitions of kinetic spin models in two dimensions. We undertake a numerical experiment performing Monte Carlo simulations of the square-lattice random-bond Ising and Blume-Capel models under a periodically oscillating magnetic field. For the case of the Blume-Capel model we analyze the universality principles of the dynamic disordered-induced continuous transition at the low-temperature regime of the phase diagram. A detailed finite-size scaling analysis indicates that both nonequilibrium phase transitions belong to the universality class of the corresponding equilibrium random Ising model.