arXiv subjects

Roberto da Silva

Publications and source records attributed to Roberto da Silva.

At least 19 recordsLinked to original sources

arXiv2026

Does the Power-Law Advantage in the Tails Outweigh the Global q-Gaussian Description?

Financial markets are complex systems whose return distributions exhibit heavy tails, traditionally described by power laws. An alternative framework based on Tsallis nonextensive statistical mechanics allows both the central region and the tails of the distribution to be represented by a single q-Gaussian functional form. In this work, we systematically compare these two descriptions across different time scales, considering stock markets from Brazil and the United States, as well as traditional assets and cryptocurrencies. The q-Gaussian parameters are estimated using the method of moments ratio, whereas the power-law parameters are obtained by maximum likelihood estimation in the asymptotic region. The quality of the fits is assessed using goodness-of-fit measures, bootstrap resampling, and the Vuong test. When the analysis is restricted exclusively to the extreme tails, the power law generally provides a better description, as expected from the asymptotic power-law behavior of the q-Gaussian itself. However, this superiority is not sufficiently pronounced to outweigh the main advantage of the q-Gaussian: its ability to provide a consistent description of the entire distribution, including the central peak, bulk, and tails, over all investigated time scales. Moreover, the evolution of the parameter $q$ offers a simple and direct characterization of aggregational Gaussianity and of the transition between heavy- and short-tailed statistical regimes, without requiring separate fits for different regions of the distribution. These results indicate that, although the power law remains particularly suitable for describing extreme events, the q-Gaussian provides a broader and more practical framework for characterizing the statistical evolution of financial returns.

physics.soc-ph↗

arXiv2026

Cumulative suspicion and absorption dynamics in an agent-based Mafia game

The Mafia game, also known as Werewolf, describes a competition between a coordinated minority whose identities are concealed and a larger good faction composed primarily of uninformed civilians attempting to identify and eliminate them. We introduce an agent-based formulation in which the daytime decision is not represented by uniform random voting. Instead, randomly paired agents modify player-specific public suspicion scores according to their roles, and one surviving player is subsequently eliminated with probability proportional to their accumulated suspicion. These scores persist throughout the game, producing a history-dependent stochastic process with two competing absorbing outcomes: elimination of the mafia or numerical parity between the mafia and the good faction. We investigate the effects of population size, initial mafia size, and the presence of perfectly informed detectives through extensive Monte Carlo simulations. In the absence of detectives, a random-execution approximation predicts that, in the dilute-mafia and early-time regime, the cumulative probability of mafia extinction behaves as $F(\tau)\sim (\tau/N)^{N_m}$, in agreement with simulations as $N_m/N$ decreases. The winning-probability curves also exhibit an empirical finite-size crossover characterized by a population scale $N_c$. Rescaling the population by $N_c$ approximately collapses the curves obtained for different initial mafia populations. Perfectly informed detectives substantially shorten mafia-survival times and introduce an additional dependence on population composition for which the same one-parameter rescaling is insufficient. The model provides a minimal connection between microscopic histories of accusation and the macroscopic absorption statistics of hidden-role games.

physics.soc-ph↗

arXiv2026

Phase Transitions and Order Parameters in Correlation Matrices: A Wishart-Ensemble Perspective on the Largest Eigenvalue

We investigate the properties of the largest eigenvalue of correlation matrices within the framework of Wishart ensembles. In this work, we propose the largest eigenvalue as an effective empirical order parameter for detecting phase transitions in chaotic and spin systems, drawing an analogy between its derivatives and thermodynamic response functions derived from the free energy, however not necessarily linked to a critical divergence originally observed in the context of phase transitions theory.

cond-mat.stat-mech↗

arXiv2026

Crossover effects on the phase transitions phenomena translated by arborecences and spectral properties

This study investigates how visibility graphs constructed from Monte Carlo Markov Chain time series of spin models capture the critical behavior of the system. More precisely, we show that this approach identifies continuous phase transitions as well as important nuances, such as crossover effects occurring in the transition from a critical line to a first-order line through a tricritical point, as observed, for example, in the Blume--Emery--Griffiths model or, in a simpler setting, in the Blume--Capel model. By applying Kirchhoff's theorem, we show that the number of spanning trees of the resulting graphs serves as a sensitive indicator of these phase transitions. Furthermore, a qualitative analysis of the adjacency matrices based on random matrix theory provides additional evidence for these phenomena. The methodology developed here can potentially be extended to the analysis of criticality in empirical time series from complex systems, such as climate, financial, and epidemiological data, where the Hamiltonian governing the dynamics is not necessarily known.

cond-mat.stat-mech↗

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

Measuring Scientific Group Performance: Integrating h-Group and Homogeneity into the $α$-Index

Ranking groups of researchers is important in several contexts and can serve many purposes such as the fair distribution of grants based on the scientist's publication output, concession of research projects, classification of journal editorial boards and many other applications in a social context. In this paper, we propose a method for measuring the performance of groups of researchers. The proposed method is called alpha-index and it is based on two parameters: (i) the homogeneity of the h-indexes of the researchers in the group; and (ii) the h-group, which is an extension of the h-index for groups. Our method integrates the concepts of homogeneity and absolute value of the h-index into a single measure which is appropriate for the evaluation of groups. We report on experiments that assess computer science conferences based on the h-indexes of their program committee members. Our results are similar to a manual classification scheme adopted by a research agency.

cs.IT↗

arXiv2025

Mean-field and Monte Carlo Analysis of Multi-Species Dynamics of agents

We propose a mean-field (MF) approximation for the recurrence relation governing the dynamics of $m$ species of particles on a square lattice, and we simultaneously perform Monte Carlo (MC) simulations under identical initial conditions to emulate the intricate motion observed in environments such as subway corridors and scramble crossings in large cities. Each species moves according to transition probabilities influenced by its respective static floor field and the state of neighboring cells. To illustrate the methodology, we analyze statistical fluctuations in the spatial distribution for $m = 1$, $m = 2$, and $m = 4$ and for different regimes of average density and biased movement. A numerical comparison is conducted to determine the best agreement between the MC simulations and the MF approximation considering a renormalization exponent $β$ that optimizes the fit between methods. Finally, we report a phenomenon we term "Gaussian-to-Gaussian" behavior, in which an initially normal distribution of particles becomes distorted due to interactions among same and opposing species, passes through a transient regime, and eventually returns to a Gaussian-like profile in the steady state, after multiple rounds of motion under periodic boundary conditions.

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↗

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↗

arXiv2024

Interplay of Reward and Size of Groups in the Optional Public Goods Game

The Optional Public Goods Game is a three-strategy game in which an individual can play as a cooperator or defector or decide not to participate. Despite its simplicity, this model can effectively represent many human social dilemmas, such as those found in the use of public services, environmental concerns, or other activities related to society. In this contribution, we present a comprehensive analysis of the conditions under which spontaneous, sustained cooperation emerges and the characteristics of these cooperative states. Through simulations, we demonstrate the conditions leading to the coexistence of the three strategies in a steady equilibrium or the alternate dominance of each strategy in a rock-paper-scissors fashion. The results identify each of the possible scenarios in terms of two key parameters: the multiplication rate of the public good game (reward) and the size of the group of potential players. We also discuss other details of the game that may influence the appearance of cycles, along with relevant characteristics of these cycles, such as the prevalence of cooperation.

physics.soc-ph↗

arXiv2024

Identifying Patterns Using Cross-Correlation Random Matrices Derived from Deterministic and Stochastic Differential Equations

Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C, 2350061 (2023)], which is directly reflected in the eigenvalues of these matrices. When these evolutions are analyzed in the mean-field regime, an important question arises: Can the Langevin equation, when translated into maps, perform the same function? Some studies suggest that this method may also capture the chaotic behavior of certain systems. In this work, we propose that the spectral properties of random matrices constructed from maps derived from deterministic or stochastic differential equations can indicate the critical or chaotic behavior of such systems. For chaotic systems, we need only the evolution of iterated Hamiltonian equations, and for spin systems, the Langevin maps obtained from mean-field equations suffice, thus avoiding the need for Monte Carlo (MC) simulations or other techniques.

cond-mat.stat-mech↗

arXiv2024

Efficient Computational method using random matrices describing critical thermodynamics

Our research highlights the effectiveness of utilizing matrices akin to Wishart matrices, derived from magnetization time series data under specific dynamics, to elucidate phase transitions and critical phenomena in the Q-state Potts model. By employing appropriate statistical methods, we not only discern second-order transitions but also differentiate weaker first-order transitions through careful analysis of the density of eigenvalues and their fluctuations. Furthermore, we investigate the method's sensitivity to stronger first-order transition points. Importantly, we establish a robust correlation between the system's actual thermodynamics and the spectral thermodynamics encapsulated within the eigenvalues. Our findings are further substantiated by correlation histograms of the time series data, revealing insightful patterns. Expanding upon our core findings, we present a didactic analysis that draws parallels between the spectral properties of criticality in a spin system and matrices intentionally imbued with correlations (a toy model). Within this framework, we observe a universal behavior characterized by the distribution of eigenvalues into two distinct groups, separated by a gap dependent on the level of correlation, influenced by temperature-induced changes in the spin system.

cond-mat.stat-mech↗

arXiv2024

Nightclub bar dynamics: statistics of serving times

In this work, we investigate the statistical properties of drink serving in a nightclub bar, utilizing a stochastic model to characterize pedestrian dynamics within the venue. Our model comprises a system of n agents moving across an underlying square lattice of size l representing the nightclub venue. Each agent can exist in one of three states: thirsty, served, or dancing. The dynamics governing the state changes are influenced by a memory time, denoted as τ, which reflects their drinking habits. Agents' movement throughout the lattice is controlled by a parameter α which measures the impetus towards/away from the bar. When α = 0, a power-law distribution emerges due to the non-objectivity of the agents. As α moves into intermediate values, an exponential behavior is observed, as it becomes possible to mitigate the drastic jamming effects in this scenario. However, for higher α values, the power-law distribution resurfaces due to increased jamming. We also demonstrate that the average concentration of served, thirsty, and dancing agents provide a reliable indicator of when the system reaches a jammed state. Subsequently, we construct a comprehensive map of the system's stationary state, supporting the idea that for high densities, α is not relevant, but for lower densities, the optimal values of measurements occurs at high values of α. To complete the analysis, we evaluate the conditional persistence, which measures the probability of an agent failing to receive their drink despite attempting to do so. In addition to contributing to the field of pedestrian dynamics, the present results serve as valuable indicators to assist commercial establishments in providing better services to their clients, tailored to the average drinking habits of their customers.

physics.soc-ph↗

arXiv2024

A spectral investigation of criticality and crossover effects in two and three dimensions: Short timescales with small systems in minute random matrices

Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper explores the applicability of such methods in investigating critical phenomena and the crossover to tricritical points within the Blume-Capel model. Through an analysis of eigenvalue mean, dispersion, and extrema statistics, we demonstrate the efficacy of these spectral techniques in characterizing critical points in both two and three dimensions. Crucially, we propose a significant modification to this spectral approach, which emerges as a versatile tool for studying critical phenomena. Unlike traditional methods that eschew diagonalization, our method excels in handling short timescales and small system sizes, widening the scope of inquiry into critical behavior.

cond-mat.stat-mech↗

arXiv2023

Exploring Transition from Stability to Chaos through Random Matrices

This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapt and apply it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance-overlap criterion for the chaos boundary at $K\approx 2.43$, reinforcing its effectiveness.

nlin.CD↗

arXiv2023

Numerical exploration of the Aging effects in spin systems

An interesting concept that has been underexplored in the context of time-dependent simulations is the correlation of total magnetization, $C(t)$%. One of its main advantages over directly studying magnetization is that we do not need to meticulously prepare initial magnetizations. This is because the evolutions are computed from initial states with spins that are independent and completely random. In this paper, we take an important step in demonstrating that even for time evolutions from other initial conditions, $C(t_{0},t)$, a suitable scaling can be performed to obtain universal power laws. We specifically consider the significant role played by the second moment of magnetization. Additionally, we complement the study by conducting a recent investigation of random matrices, which are applied to determine the critical properties of the system. Our results show that the aging in the time series of magnetization influences the spectral properties of matrices and their ability to determine the critical temperature of systems.

cond-mat.stat-mech↗