arXiv subjects

H. A. Fernandes

Publications and source records attributed to H. A. Fernandes.

8 recordsLinked to original sources

arXiv2020

Phase diagrams of the ZGB model on random networks

In this work, we revisited the ZGB model in order to study the behavior of its phase diagram when two well-known random networks play the role of the catalytic surfaces: the Random Geometric Graph and the Erdös-Rényi network. The connectivity and, therefore, the average number of neighbors of the nodes of these networks can vary according to their control parameters, the neighborhood radius $α$ and the linking probability $p$, respectively. In addition, the catalytic reactions of the ZGB model are governed by the parameter $y$, the adsorption rate of carbon monoxide molecules on the catalytic surface. So, to study the phase diagrams of the model on both random networks, we carried out extensive steady-state Monte Carlo simulations in the space parameters ($y,α$) and ($y,p$) and showed that the continuous phase transition is greatly affected by the topological features of the networks while the discontinuous one remains present in the diagram throughout the interval of study.

cond-mat.stat-mech↗

arXiv2019

Mapping the phase transitions of the ZGB model with inert sites via nonequilibrium refinement methods

In this paper, we revisit the ZGB model and explore the effects of the presence of inert sites on the catalytic surface. The continuous and discontinuous phase transitions of the model are studied via time-dependent Monte Carlo simulations. In our study, we are concerned with building a refinement procedure, based on a simple concept known as coefficient of determination $r$, in order to find the possible phase transition points given by the two parameters of the model: the adsorption rates of carbon monoxide, $y$, and the density of inert sites, $ρ_{is}$. First, we obtain $10^6$ values of $r$ by sweeping the whole set of possible values of the parameters with an increment $10^{-3}$, i.e., $0 \leq y \leq 1$ and $0 \leq ρ_{is} \leq 1$ with $Δy=Δρ_{is}=10^{-3}$. Then, with the possible phase transition points in hand, we turn our attention to some fixed values of $ρ_{is}$ and perform a more detailed refinement considering larger lattices and increasing the increment $Δy$ by one order of magnitude to estimate the critical points with higher precision. Finally, we estimate the static critical exponents $β$, $ν_{\parallel}$, and $ν_{\perp}$, as well as the dynamic critical exponents $z$ and $θ$.

cond-mat.stat-mech↗

arXiv2017

A comparative study of the dynamic critical behavior of the four-state Potts like models

We investigate the short-time critical dynamics of the Baxter-Wu (BW) and $n=3$ Turban (3TU) models to estimate their global persistence exponent $θ_{g}$. We conclude that this new dynamical exponent can be useful in detecting differences between the critical behavior of these models which are very difficult to obtain in usual simulations. In addition, we estimate again the dynamical exponents of the four-state Potts (FSP) model in order to compare them with results previously obtained for the BW and 3TU models and to decide between two sets of estimates presented in the current literature. We also revisit the short-time dynamics of the 3TU model in order to check if, as already found for the FSP model, the anomalous dimension of the initial magnetization $x_{0}$ could be equal to zero.

cond-mat.stat-mech↗

arXiv2016

Non-equilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line

We investigate the short-time universal behavior of the two dimensional Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo Simulations. First, as preparatory results, we obtain the critical parameters by searching the optimal power law decay of the magnetization. Thus, the dynamic critical exponents $θ_{m}$ and $θ_{p}$, related to the magnetic and electric order parameters, as well as the persistence exponent $θ_{g}$, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent $z$ and the static critical exponents $β$ and $ν$ for both order parameters. We propose a refined method to estimate the static exponents that considers two different averages: one that combines an internal average using several seeds with another which is taken over geographic variations in the power laws. Moreover, we also performed the bootstrapping method for a complementary analysis. Our results show that the ratio $β/ν$ exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.

cond-mat.stat-mech↗

arXiv2015

Mechanical strain in capped and uncapped self-assembled Ge/Si quantum dots

In this study we numerically calculate the spatial profile of mechanical strain on self-assembled germanium (Ge) quantum dots (QDs) grown on a silicon (Si) substrate. Although the topic has been exhaustively studied, interesting features have not been explained or even mentioned in the literature yet. We studied the effect of the cap layer considering two cases: capped QDs (where a Si cap is present above the Ge QDs) and uncapped QDs (where no Si is present above the Ge QDs). We observed that Ge in the capped QDs is more strained compared with the the uncapped QDs. This expected effect is attributed to the additional tension from the Si cap layer. However, the situation is opposite for the Si substrate, it is more strained in the uncapped QD because the Ge layer is less strained in this case. We also calculated the band-edge alignment for the electrons and holes.

cond-mat.mtrl-sci↗

arXiv2006

Global persistence exponent of the double-exchange model

We obtained the global persistence exponent $θ_g$ for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent $θ_g$ by following the time evolution of probability $P(t)$ that the order parameter of the model does not change its sign up to time $t$ $[P(t)\thicksim t^{-θ_g}]$. Afterwards, that exponent was estimated through the scaling collapse of the universal function $L^{θ_g z} P(t)$ for different lattice sizes. Our results for both approaches are in very good agreement each other.

cond-mat.stat-mech↗

arXiv2006

An alternative order parameter for the 4-state Potts model

We have investigated the dynamic critical behavior of the two-dimensional 4-state Potts model using an alternative order parameter first used by Vanderzande [J. Phys. A: Math. Gen. \textbf{20}, L549 (1987)] in the study of the Z(5) model. We have estimated the global persistence exponent $θ_g$ by following the time evolution of the probability $P(t)$ that the considered order parameter does not change its sign up to time $t$. We have also obtained the critical exponents $θ$, $z$, $ν$, and $β$ using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature.

cond-mat.stat-mech↗

arXiv2006

Short-time behavior of a classical ferromagnet with double-exchange interaction

We investigate the critical dynamics of a classical ferromagnet on the simple cubic lattice with double-exchange interaction. Estimates for the dynamic critical exponents $z$ and $θ$ are obtained using short-time Monte Carlo simulations. We also estimate the static critical exponents $ν$ and $β$ studying the behavior of the samples at an early time. Our results are in good agreement with available estimates and support the assertion that this model and the classical Heisenberg model belong to the same universality class.

cond-mat.stat-mech↗