Henrique A. Fernandes

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.

Global persistence exponent of the double-exchange model.

We obtained the global persistence exponent for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent theta(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) approximately t(-theta(g)]. Afterwards, that exponent was estimated through the scaling collapse of the universal function L(theta(g)(z)P(t) for different lattice sizes. Our results for both approaches are in very good agreement with each other.

Nonequilibrium scaling explorations on a two-dimensional 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. In addition, 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 Fateev-Zamolodchikov (FZ) point. First, 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≈2.28 very close to the four-state Potts model (z≈2.29).

Novel considerations about the non-equilibrium regime of the tricritical point in a metamagnetic model: Localization and tricritical exponents

Abstract We have investigated the time-dependent regime of a two-dimensional metamagnetic model at its tricritical point via Monte Carlo simulations. First, we obtained the temperature and magnetic field corresponding to the tricritical point of the model by using a refinement process based on optimization of the coefficient of determination in the log–log fit of magnetization decay as a function of time. With these estimates in hand, we obtained the dynamic tricritical exponents θ and z and the static tricritical exponents ν and β by using the universal power-law scaling relations for the staggered magnetization and its moments at an early stage of the dynamic evolution. Our results at the tricritical point confirm that this model belongs to the two-dimensional Blume–Capel model universality class for both static and dynamic behaviors, and they also corroborate the conjecture of Janssen and Oerding for the dynamics of tricritical points.

Nonequilibrium 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 temporal 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.

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.

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.

Highly detailed computational study of a surface reaction model with diffusion: Four algorithms analyzed via time-dependent and steady-state Monte Carlo simulations

Abstract In this work, we present an extensive computational study on the Ziff–Gulari–Barshad (ZGB) model extended in order to include the spatial diffusion of oxygen atoms and carbon monoxide molecules, both adsorbed on the surface. In our approach, we consider two different protocols to implement the diffusion of the atoms/molecules and two different ways to combine the diffusion and adsorption processes resulting in four different algorithms. The influence of the diffusion on the continuous and discontinuous phase transitions of the model is analyzed through two very well established methods: the time-dependent Monte Carlo simulations and the steady-state Monte Carlo simulations. We also use an optimization method based on a concept known as coefficient of determination to construct color maps and obtain the phase transitions when the parameters of the model vary. This method was proposed recently to locate nonequilibrium second-order phase transitions and has been successfully used in both systems: with defined Hamiltonian and with absorbing states. The results obtained via time-dependent Monte Carlo simulation along with the coefficient of determination are corroborated by traditional steady-state Monte Carlo simulations also performed for the four algorithms. Finally, we analyze the finite-size effects on the results, as well as, the influence of the number of runs on the reliability of our estimates.

Statistics, distillation, and ordering emergence in a two-dimensional stochastic model of particles in counterflowing streams

In this paper, we propose a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework that describes the transport in random systems by taking into account two different scenarios: particles can work as mobile obstacles, whereas particles of one species move in the opposite direction to the particles of the other species, or particles of a given species work as fixed obstacles remaining in their places during the time evolution. We conduct a detailed study about the statistics concerning the crossing time of particles, as well as the effects of the lateral transitions on the time required to the system reaches a state of complete geographic separation of species. The spatial effects of jamming are also studied by looking into the deformation of the concentration of particles in the two-dimensional corridor. Finally, we observe in our study the formation of patterns of lanes which reach the steady state regardless of the initial conditions used for the evolution. A similar result is also observed in real experiments involving charged colloids motion and simulations of pedestrian dynamics based on Langevin equations, when periodic boundary conditions are considered (particles counterflow in a ring symmetry). The results obtained through Monte Carlo simulations and numerical integrations are in good agreement with each other. However, differently from previous studies, the dynamics considered in this work is not Newton-based, and therefore, even artificial situations of self-propelled objects should be studied in this first-principles modeling.

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 θg. 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 x0 could be equal to zero.