arXiv subjects

Henrique Almeida Fernandes

Publications and source records attributed to Henrique Almeida Fernandes.

7 recordsLinked to original sources

arXiv2025

Revisiting the Contact Model with Diffusion Beyond the Conventional Methods

The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility/diffusion on criticality have been preliminarily investigated, they remain incompletely understood. In this work, we examine how the critical rate of the model varies with the probability of particle mobility. By analyzing different stochastic evolutions of the system, we employ two modern approaches: 1) Random Matrix Theory (RMT): By building on the success of RMT, particularly Wishart-like matrices, in studying statistical physics of systems with up-down symmetry via magnetization dynamics [R. da Silva, IJMPC 2022], we demonstrate its applicability to models with an absorbing state. 2) Optimized Temporal Power Laws: By using short-time dynamics, we optimize power laws derived from ensemble-averaged evolutions of the system. Both methods consistently reveal that the critical rate decays with mobility according to a simple Belehradek function. Additionally, a straightforward mean-field analysis supports the decay of the critical parameter with mobility, although it predicts a simpler linear dependence.

cond-mat.stat-mech↗

arXiv2025

Unveiling the hidden weak universality of the ZGB model

In this work, we revisited the Ziff-Gullari-Barshad (ZGB) model in order to investigate its critical behavior when carbon monoxide (CO) molecules are allowed to desorb from the catalytic surface. As shown by several authors, when this kind of desorption takes place, the first-order phase transition of the standard model disappears, and an Ising-like critical point is found for a very small value of the desorption rate. However, our time-dependent Monte Carlo simulations reveal that, instead of a single critical point, there exists a critical line that encompasses multiple universality classes, passing through the three- and four-state Potts points, as well as, the Ising one, resulting in an unprecedented critical line of weak universality.

cond-mat.stat-mech↗

arXiv2022

Topological transition in a coupled dynamic in random networks

In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better understand the two observed phases, so we use another network structure (the so called random geometric graph - RGG) together with other metrics borrowed from network science. We observed a topological transition on the two associated networks, which are subgraphs of the full network. As the links have two possible states (friendly and non-friendly), we defined each associated network as composed of only one type of link. The (non) friendly associated network has (non) friendly links only. This topological transition was observed from the domain distribution of each associated network between the two phases of the system (absorbing and active). We also showed that another metric from network science called modularity (or assortative coefficient) can also be used as order parameter, giving the same phase diagram as the original order parameter from the seminal work. On the absorbing phase the absolute value of the modularity for each associated network reaches a maximum value, while on the active phase they fall to the minimum value.

physics.soc-ph↗

arXiv2018

Epidemic SIR model on a face-to-face interaction network: new mobility induced phase transitions

In this work, we study the epidemic SIR model on a system which takes into consideration face-to-face interaction networks. This approach has been used as prototype to describe people interactions in different kinds of social organizations and, here, it is considered by means of three features of human interactions: the mobility, the duration of the interaction among people, and the dependence of the number of interactions of each person on the time evolution of the system. For this purpose, the initial configuration of the system is set as a regular square lattice where the nodes are the individuals which, in turn, are able to move in a random walk along the network. So, the connectivity among the individuals evolve with time and is defined by the positions of the individuals at each iteration. In a time unit, each individual is able move up to a distance $v$ creating different networks along the time evolution of the system. In addition, the individuals are interacting with each other only if they are within the interaction distance $δ$ and, in this case, they are considered as neighbors. If a given individual is interacting with other ones, he performs the random walk with a diffusion probability $ω$. Otherwise, the diffusion occurs with probability 1. The study was carried out through non-equilibrium Monte Carlo Simulations and we take into account the asynchronous updating scheme. The results show that, for a given $v>0$, there exist a critical line in the $(c, δ)$ space, where $c$ is the immunization rate. We also obtain the dynamic critical exponent $θ$ for some points belonging to this line and show that this model does not belong to the directed percolation universality class.

physics.soc-ph↗

arXiv2018

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

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 analysed 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 analyse the finite-size effects on the results, as well as, the influence of the number of runs on the reliability of our estimates.

cond-mat.stat-mech↗

arXiv2017

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

In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile obstacles, whereas particles of one species move in opposite direction to the particles of the other species, or they can work as fixed obstacles remaining in their places during the time evolution. We conducted 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 were also studied by looking into the deformation of the concentration of particles in the two-dimensional corridor. Finally, we observed in our study the formation of patterns of lanes which reach the steady state regardless 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 numerical 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-principle modeling.

cond-mat.soft↗

arXiv2015

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

We have investigated the time-dependent regime of a two-dimensional metamagnetic model at its tricritical point via Monte Carlo simulations. First of all, 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 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 early stage of the dynamic evolution. Our results at tricritical point confirm that this model belongs to the two-dimensional Blume-Capel model universality class for both static and dynamic behaviors, and also they corroborate the conjecture of Janssen and Oerding for the dynamics of tricritical points.

cond-mat.stat-mech↗