arXiv subjects

Henrique A. Fernandes

Publications and source records attributed to Henrique A. Fernandes.

13 recordsLinked to original sources

arXiv2025

Phase Diagrams of the YK Surface-Reaction Model on 2D lattices with Exchange Diffusion

In this work, we investigate the phase diagrams of the Yaldram and Khan catalytic surface model on square and hexagonal lattices when exchange diffusion is allowed for carbon monoxide (CO) and nitrogen (N) atoms. To reach our goal, we carried out steady-state Monte Carlo (MC) simulations over $4\times 10^5$ points, for both lattices, in order to obtain a framework of the steady reactive state of the model for different values of the nitric oxide dissociation rate, $r_{NO}$. The results show the emergence of steady reactive state for certain values of $r_{NO}$ and of exchange diffusion rate $x$ when the simulations take place on square lattices. Our findings on the hexagonal lattice also show that the diffusion of these species favors the appearance of the active phase for values of $r_{NO}$ lower than that found for the standard model. In addition, we observed that the system possesses a continuous phase transition and a discontinuous one separating the active phase from absorbing states for both lattices, except for $r_{NO}=1$ in which the continuous phase transition is destroyed and a steady reactive state emerges from the beginning since very small values of $x$.

cond-mat.stat-mech↗

arXiv2025

The number of spanning trees as an indicator of critical phenomena: When Kirchhoff meets Ising

Visibility graphs are spatial interpretations of time series. When derived from the time evolution of physical systems, the graphs associated with such series may exhibit properties that can reflect aspects such as ergodicity, criticality, or other dynamical behaviors. It is important to describe how the criticality of a system is manifested in the structure of the corresponding graphs or, in a particular way, in the spectra of certain matrices constructed from them. In this paper, we show how the critical behavior of an Ising spin system manifests in the spectra of the adjacency and Laplacian matrices constructed from an ensemble of time evolutions simulated via Monte Carlo (MC) Markov Chains, even for small systems and short MC steps. In particular, we show that the number of spanning trees -- or its logarithm -- , which represents a kind of \emph{structural entropy} or \emph{topological complexity} here obtained from Kirchhoff's theorem, can, in an alternative way, describe the criticality of the spin system. These findings parallel those obtained from the spectra of correlation matrices, which similarly encode signatures of critical and chaotic behavior.

cond-mat.stat-mech↗

arXiv2025

Topology induced modifications in the critical behavior of the Yaldram Khan catalytic reaction model

In this work, we investigated how the use of complex networks as catalytic surfaces can affect the phase diagram of the Yaldram-Khan model, as well as how the order of the phase transitions present in the seminal work behaves when the randomness is added to the model. The study was conducted by taking into consideration two well-known random networks, the Erdos-Renyi network (ERN), with its long-range randomness, and the random geometric graph (RGG), with its spatially constrained randomness. We perform extensive steady-state Monte Carlo simulations assuming the NO dissociation rate is equal to 1 and show the behavior of the reactive window as function of the average degree of the networks. Our results also show that, different from the ERN, which preserves the nature of the phase transitions of the original model for all considered average degrees, the RGG seems to have two second-order phase transitions for small values of average degree.

cond-mat.stat-mech↗

arXiv2021

A physics-based algorithm to perform predictions in football leagues

In this work, we extended a stochastic model for football leagues based on the team's potential [R. da Silva et al. Comput. Phys. Commun. \textbf{184} 661--670 (2013)] for making predictions instead of only performing a successful characterization of the statistics on the punctuation of the real leagues. Our adaptation considers the advantage of playing at home when considering the potential of the home and away teams. The algorithm predicts the tournament's outcome by using the market value or/and the ongoing team's performance as initial conditions in the context of Monte Carlo simulations. We present and compare our results to the worldwide known SPI predictions performed by the "FiveThirtyEight" project. The results show that the algorithm can deliver good predictions even with a few ingredients and in more complicated seasons like the 2020 editions where the matches were played without fans in the stadiums.

physics.soc-ph↗

arXiv2018

Investigating the nonequilibrium aspects of long-range Potts model: refinement of critical temperatures and raw exponents

In this work, we analyse the $q-$state Potts model with long-range interactions through nonequilibrium scaling relations commonly used when studying short-range systems. We determine the critical temperature via an optimization method for short-time Monte Carlo simulations. The study takes into consideration two different boundary conditions and three different values of range parameters of the couplings. We also present estimates of some critical exponents, named as raw exponents for systems with long-range interactions, which confirm the non-universal character of the model. Finally, we provide some preliminary results addressing the relations between the raw exponents and the exponents obtained for systems with short-range interactions. The results assert that the methods employed in this work are suitable to study the considered model and can easily be adapted to other systems with long-range interactions.

cond-mat.stat-mech↗

arXiv2018

Unveiling the ZGB model with $CO$ desorption: a single model with two universality classes?

We study the behavior of the phase transitions of the Ziff-Gullari-Barshad (ZGB) model when the $CO$ molecules are adsorbed on the catalytic surface with a rate $y$ and desorbed from the surface with a rate $k$. We employ large-scale nonequilibrium Monte Carlo simulations along with an optimization technique based on the coefficient of determination, in order to obtain an overview of the phase transitions of the model in the whole spectrum of $y$ and $k$: ($0\leq y\leq 1$ and $0\leq k\leq 1$) with precision $Δy=Δk=0.001$. Sucessive refinements reveal a region of points belonging to the directed percolation universality class whereas the exponents $θ$ and $β/ν_{\parallel }$ obtained agree with those of this universality class. On the other hand, the effects of allowing the $CO$ desorption from the lattice on the discontinuous phase transition point of the original ZGB model suggest the emergence of an Ising-like point previously predicted in Ref. \cite{tome1993}. We show that such a point appears after a sequence of two lines of pseudo-critical points which leads to a unique peak of the coefficient of determination curve in $y_{c}=0.554$ and $k_{c}=0.064$. In this point, the exponent $θ$ agrees with the value found for Ising model.

cond-mat.stat-mech↗

arXiv2018

When and how much the altruism impacts your privileged information? Proposing a new paradigm in game theory: The boxers game

In this work, we proposed a new $N$-person game in which the players can bet on two options, for example represented by two boxers. Some of the players have privileged information about the boxers and part of them can provide this information to uninformed players. However, this information may be true if the informed player is altruist or false if he is selfish. So, in this game, the players are divided in three categories: informed and altruist players, informed and selfish players, and uninformed players. By considering the matchings ($N/2$ distinct pairs of randomly chosen players) and that the payoff of the winning group follows aspects captured from two important games, the public goods game and minority game, we showed quantitatively and qualitatively how the altruism can impact on the privileged information. We localized analytically the regions of positive payoffs which were corroborated by numerical simulations performed for all values of information and altruism densities given that we know the information level of the informed players. Finally, in an evolutionary version of the game ,we showed that the gain of the informed players can get worse if we adopted the following procedure: the players increase their investment for situations of positive payoffs, and decrease their investment when negative payoffs occur.

cond-mat.stat-mech↗

arXiv2017

Analysis of etching at a solid-solid interface

We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height variance (roughness). We apply this method to the etching model in 1 + 1 dimensions, and then we obtain the roughness exponent. Using this in conjunction with the Galilean invariance we obtain the other exponents, which perfectly match the numerical results obtained from simulations. These exponents are exact, and they are the same as those exhibited by the Kardar-Parisi-Zhang (KPZ) model for this dimension. Therefore, our results provide proof for the conjecture that the etching and KPZ models belong to the same universality class. Moreover, the method is general, and it can be applied to other cellular automata models.

cond-mat.stat-mech↗

arXiv2017

A new look on the stabilization of inverted pendulum with parametric excitation and large random frequencies: analytical and numerical approaches

In this paper we explore the stability of an inverted pendulum with generalized parametric excitation described by a superposition of $N$ sines with different frequencies and phases. We show that when the amplitude is scaled with the frequency we obtain the stabilization of the real inverted pendulum, i.e., with values of $g$ according to planet Earth ($g\approx 9.8$m/s$^{2}$) for high frequencies. By randomly sorting the frequencies, we obtain a critical amplitude in light of perturbative theory in classical mechanics which is numerically tested by exploring its validity regime in many alternatives. We also analyse the effects when different values of $N$ as well as the pendulum size $l$ are taken into account.

physics.class-ph↗

arXiv2016

An alternative method to characterize first- and second-order phase transitions in surface reaction models

In this work, we revisited the Ziff-Gulari-Barshad (ZGB) model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We used a method proposed recently to locate the non-equilibrium second-order phase transitions and that has been successfully used in systems with defined Hamiltonians and with absorbing states. This method, which is based on optimization of the coefficient of determination of the order parameter, was able to characterize the second-order phase transition of the model, as well as its upper spinodal point, a pseudo-critical point located near the first-order transition. The static critical exponents $β$, $ν_{\parallel }$, and $ν_{\perp }$, as well as the dynamic critical exponents $θ$ and $z$ for the second-order point were also estimated and are in excellent agreement with results found in literature.

cond-mat.stat-mech↗

arXiv2014

A study of the influence of the mobility on the phase transitions of the synchronous SIR model

By using an appropriate version of the synchronous SIR model, we studied the effects of dilution and mobility on the critical immunization rate. We showed that, by applying time-dependent Monte Carlo (MC) simulations at criticality, and taking into account the optimization of the power law for the density of infected individuals, the critical immunization necessary to block the epidemic in two-dimensional lattices decreases as dilution increases with a logarithmic dependence. On the other hand, the mobility minimizes such effects and the critical immunizations is greater when the probability of movement of the individuals increases.

physics.soc-ph↗

arXiv2014

Nonequilibrium scaling explorations on a 2D Z(5)-symmetric model

We have investigated the dynamic critical behavior of the two-dimensional Z(5)-symmetric spin model by using short-time Monte Carlo (MC) simulations. We have obtained estimates of some critical points in its rich phase diagram and included, among the usual critical lines the study of first-order (weak) transition by looking into the order-disorder phase transition. Besides, we also investigated the soft-disorder phase transition by considering empiric methods. A study of the behavior of $β/νz$ along the self-dual critical line has been performed and special attention has been devoted to the critical bifurcation point, or FZ (Fateev-Zamolodchikov) point. Firstly, by using a refinement method and taking into account simulations out-of-equilibrium, we were able to localize parameters of this point. In a second part of our study, we turned our attention to the behavior of the model at the early stage of its time evolution in order to find the dynamic critical exponent z as well as the static critical exponents $β$ and $% ν$ of the FZ-point on square lattices. The values of the static critical exponents and parameters are in good agreement with the exact results, and the dynamic critical exponent $z\approx 2.28$ very close of the 4-state Potts model ($z\approx 2.29$).

cond-mat.stat-mech↗

arXiv2012

An analytical formulation for roughness based on celular automata

We present a method to derive the analytical expression of the roughness of a fractal surface whose dynamics is ruled by cellular automata. Starting from the automata, we write down the the time derivative of the height's average and variance. By assuming the equiprobability of the surface configurations and taking the limit of large substrates we find the roughness as a function of time. As expected, the function behaves as $t^β$ when $t\ll t_\times$ and saturate at $w_s$ when $t\gg t_\times$. We apply the methodology to describe the etching model \citep{Bernardo}, however, the value of $β$ we obtained are not the one predicted by the KPZ equation and observed in numerical experiments. That divergence may be due to the equiprobability assumption. We redefine the roughness with an exponent that compensate the nonuniform probability generated by the celular automata, resulting in an expression that perfectly matches the experimental results.

nlin.CG↗