arXiv subjects

W. G. Dantas

Publications and source records attributed to W. G. Dantas.

At least 19 recordsLinked to original sources

arXiv2026

Coarsening in the long-range Persistent Voter Model

We investigate the coarsening kinetics in a long-range variant of the Persistent Voter Model in space dimensions $d=1$ and 2. In this model, agents can hold two confidence levels, normal and zealot. Normal agents imitate another opinion chosen at a distance $r$ with probability $P(r) \propto r^{-α}$, with $α>d$. On the contrary, while in the zealot state, agents keep their own opinion. Normal (zealot) agents can become zealots (normal) if their opinion is equal (different) to that of the chosen neighbour. Through numerical simulations we show that, for any values of $α$, the model belongs to the same universality class of the long-range Ising model quenched to a small (non-zero) temperature, similarly to what was already known for the nearest-neighbor case. For the one-dimensional case, we further develop an analytical treatment, which reproduces the $α$-dependence of the correlation length and the functional form of the correlation function. These results not only confirm that the introduction of opinion inertia mitigates the strong interfacial noise present in the Voter model, thus reinstating the basic kinetic mechanism of the Ising model, but also expand the applicability of this correspondence.

cond-mat.stat-mech↗

arXiv2025

Opinion inertia and coarsening in the Persistent Voter model

We consider the Persistent Voter model (PVM), a variant of the Voter model (VM) that includes transient, dynamically-induced zealots. Due to peer reinforcement, the internal confidence $η_i$ of a normal voter increases by steps of size $Δη$ and once it gets above a given threshold, it becomes a zealot. Then, its opinion remains frozen until enough interactions with the opposite opinion occur and its confidence is reset. No longer a zealot, the regular voter may change opinion once again. This opinion inertia mechanism, albeit simplified, is responsible for an effective surface tension and the PVM has a crossover from a fluctuation-driven dynamics, as in the VM, to a curvature-driven one, as in the Ising Model at low temperature (IM0). The average time $τ$ to attain consensus is non-monotonic on $Δη$ and has a minimum at $Δη_{\min}$. In this paper we clarify the mechanisms that accelerate the system towards consensus close to $Δη_{\min}$. Close to the crossover at $Δη_{\min}$, the intermediate region around the domains where the regular voters accumulate (the active region, AR) is large and the surface tension, albeit small, is still enough to keep the shape and reduce the fragmentation of the domains. The large size of the AR in the region of $Δη_{\min}$ has two important effects that accelerates the dynamics. First, it dislodges the zealots in the bulk of the domains and second, it maximally suppresses the slowly-evolving stripes that normally form in Ising-like models. This suggests the importance of understanding the role of the AR, where the change of opinion is facilitated, and the interplay between regular voters and zealots when attempting to disrupt polarized states.

physics.soc-ph↗

arXiv2025

Coarsening in the Persistent Voter Model: analytical results

We investigate the coarsening dynamics of a simplified version of the persistent voter model in which an agent can become a zealot -- i.e. resistent to change opinion -- at each step, based on interactions with its nearest neighbors. We show that such a model captures the main features of the original, non-Markovian, persistent voter model. We derive the governing equations for the one-point and two-point correlation functions. As these equations do not form a closed set, we employ approximate closure schemes, whose validity was confirmed through numerical simulations. Analytical solutions to these equations are obtained and well agree with the numerical results.

cond-mat.stat-mech↗

arXiv2022

Entropy of rigid k-mers on a square lattice

Using the transfer matrix technique, we estimate the entropy for a gas of rods of sizes equal to k (named k-mers), which cover completely a square lattice. Our calculations were made considering three different constructions, using periodical and helical boundary conditions. One of those constructions, which we call Profile Method, was based on the calculations performed by Dhar and Rajesh [Phys. Rev. E 103, 042130 (2021)] to obtain a lower limit to the entropy of very large chains placed on the square lattice. This method, so far as we know, was never used before to define the transfer matrix, but turned out to be very useful, since it produces matrices with smaller dimensions than those obtained using other approaches. Our results were obtained for chain sizes ranging from k=2 to k=10 and they are compared with results already available in the literature. In the case of dimers ($k=2$) our results are compatible with the exact result, for trimers ($k=3$), recently investigated by Ghosh et al [Phys. Rev. E 75, 011115 (2007)] also our results were compatible, the same happening for the simulational estimates obtained by Pasinetti et al [Physical Review E 104, 054136 (2021)] in the whole range of rod sizes. Our results are consistent with the asymptotic expression for the behavior of the entropy as a function of the size $k$, proposed by Dhar and Rajesh [Phys. Rev. E 103, 042130 (2021)] for very large rods (k>>1).

cond-mat.stat-mech↗

arXiv2022

Curvature-driven growth and interfacial noise in the voter model with self-induced zealots

We introduce a variant of the voter model in which agents may have different degrees of confidence on their opinions. Those with low confidence are normal voters whose state can change upon a single contact with a different neighboring opinion. However, confidence increases with opinion reinforcement and, above a certain threshold, these agents become zealots that do not change opinion. We show that both strategies, normal voters and zealots, may coexist, leading to a competition between two different kinetic mechanisms: curvature-driven growth and interfacial noise. The kinetically constrained zealots are formed well inside the clusters, away from the different opinions at the surfaces that help keep the confidence not so high. Normal voters concentrate in a region around the interfaces and their number, that is related with the distance between the surface and the zealotry bulk, depends on the rate the confidence changes. Despite this interface being rough and fragmented, typical of the voter model, the presence of zealots in the bulk of these domains, induces a curvature-driven dynamics, similar to the low temperature coarsening behavior of the non-conserved Ising model after a temperature quench.

cond-mat.stat-mech↗

arXiv2020

Skepticism and rumor spreading: the role of spatial correlations

Critical thinking and skepticism are fundamental mechanisms that one may use to prevent the spreading of rumors, fake-news and misinformation. We consider a simple model in which agents without previous contact with the rumor, being skeptically oriented, may convince spreaders to stop their activity or, once exposed to the rumor, decide not to propagate it as a consequence, for example, of fact-checking. We extend a previous, mean-field analysis of the combined effect of these two mechanisms, active and passive skepticism, to include spatial correlations. This can be done either analytically, through the pair approximation, or simulating an agent-based version on diverse networks. Our results show that while in mean-field there is no coexistence between spreaders and susceptibles (although, depending on the parameters, there may be bistability depending on the initial conditions), when spatial correlations are included, because of the protective effect of the isolation provided by removed agents, coexistence is possible.

physics.soc-ph↗

arXiv2019

Using Nanoresonators with Robust Chaos as HRNGs

In this paper, we investigate theoretically the potential of a nanoelectromechanical suspended beam resonator excited by two-external frequencies as a hardware random number generator (HRNG). This system exhibits robust chaos, which is usually required for practical applications of chaos. Taking advantage of the robust chaotic oscillations we consider the beam position as a possible random variable and perform tests to check its randomness. The beam position collected at fixed time intervals is used to create a set of values that is a candidate for a random sequence of numbers. To determine how close to a random sequence this set is we perform several known statistical tests of randomness. The performance of the random sequence in the simulation of two relevant physical problems, the random walk and the Ising model, is also investigated. An excellent overall performance of the system as a random number generator is obtained.

physics.class-ph↗

arXiv2017

Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares

We study a model of semi-flexible self-avoiding trails, where the lattice paths are constrained to visit each lattice edge at most once, with configurations weighted by the number of collisions, crossings and bends, on a Husimi lattice built with squares. We find a rich phase diagram with five phases: a non-polymerised phase (${\bf NP}$), low density (${\bf P1}$) and high density (${\bf P2}$) polymerised phases, and, for sufficiently large stiffness, two additional anisotropic (nematic) (${\bf AN1}$ and ${\bf AN2}$) polymerised phases within the ${\bf P1}$ phase. Moreover, the {\bf AN1} phase which shows a broken symmetry with a preferential direction, is separated from the ${\bf P1}$ phase by the other nematic ${\bf AN2}$ phase. Although this scenario is similar to what was found in our previous calculation on the Bethe lattice, where the ${\bf AN-P1}$ transition was discontinuous and critical, the presence of the additional nematic phase between them introduces a qualitative difference. Other details of the phase diagram are that a line of tri-critical points may separate the ${\bf P1}-{\bf P2}$ transition surface into a continuous and a discontinuous portion, and that the same may happen at the ${\bf NP}-{\bf P1}$ transition surface, details of which depend on whether crossings are allowed or forbidden. A critical end-point line is also found in the phase diagram.

cond-mat.stat-mech↗

arXiv2016

Grand-canonical solution of semi-flexible self-avoiding trails on the Bethe lattice

We consider a model of semi-flexible interacting self-avoiding trails (sISAT's) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting self-avoiding walks (SASAW) to investigate the collapse transition of polymers, with the attractive interactions being on site, as opposed to nearest-neighbor interactions in SASAW. The grand-canonical version of the sISAT model is solved on a four-coordinated Bethe lattice, and four phases appear: non-polymerized (NP), regular polymerized (P), dense polymerized (DP) and anisotropic nematic (AN), the last one present in the phase diagram only for sufficiently stiff chains. The last two phases are dense, in the sense that all lattice sites are visited once in AN phase and twice in DP phase. In general, critical NP-P and DP-P transition surfaces meet with a NP-DP coexistence surface at a line of bicritical points. The region in which the AN phase is stable is limited by a discontinuous critical transition to the P phase, and we study this somewhat unusual transition in some detail. In the limit of rods, where the chains are totally rigid, the P phase is absent and the three coexistence lines (NP-AN, AN-DP, and NP-DP) meet at a triple point, which is the endpoint of the bicritical line.

cond-mat.stat-mech↗

arXiv2016

Fingerprint of Tsallis statistics in cosmic ray showers

We investigate the impact of the Tsallis non extensive statistics introduced by intrinsic temperature fluctuations in p-Air ultra high energy interactions on observables of cosmic ray showers, such as the slant depth of the maximum Xmax and the muon number on the ground $n_μ$. The results show that these observables are significantly affected by temperature fluctuations and agree qualitatively with the Heitler model predictions.

hep-ph↗

arXiv2008

Simulational study for the crossover in the generalized contact process with diffusion

In a recent work, Dantas and Stilck studied a model that generalizes the contact process model with diffusion. Our approach, based on the supercritical expansion, showed that for a weak diffusion regime the crossover exponent between the directed percolation and compact directed percolation universality classes was $ϕ\approx 2$. However this approach did not work for reduced diffusion rates higher than $D\approx 0.3$, where $0\leq D\leq 1$ and D=1 corresponds to an infinite diffusion rate. Thus, in the present work we estimate this crossover exponent for higher diffusion rates using a numerical simulation approach.

cond-mat.stat-mech↗

arXiv2007

Asymptotic behavior of the entropy of chains placed on stripes

By using the transfer matrix approach, we investigate the asymptotic behavior of the entropy of flexible chains with $M$ monomers each placed on stripes. In the limit of high density of monomers, we study the behavior of the entropy as a function of the density of monomers and the width of the stripe, inspired by recent analytical studies of this problem for the particular case of dimers (M=2). We obtain the entropy in the asymptotic regime of high densities for chains with $M=2,..,9$ monomers, as well as for the special case of polymers, where $M\to\infty$, and find that the results show a regular behavior similar to the one found analytically for dimers. We also verify that in the low-density limit the mean-field expression for the entropy is followed by the results from our transfer matrix calculations.

cond-mat.stat-mech↗

arXiv2007

A comparative study for the pair-creation contact process using series expansions

A comparative study between two distinct perturbative series expansions for the pair-creation contact process is presented. In contrast to the ordinary contact process, whose supercritical series expansions provide accurate estimates for its critical behavior, the supercritical approach does not work properly when applied to the pair-creation process. To circumvent this problem a procedure is introduced in which one-site creation is added to the pair-creation. An alternative method is the generation of subcritical series expansions which works even for the case of the pure pair-creation process. Differently from the supercritical case, the subcritical series yields estimates that are compatible with numerical simulations.

cond-mat.stat-mech↗

arXiv2007

Revisiting the one-dimensional diffusive contact process

In this work we study the one-dimensional contact process with diffusion using two different approaches to research the critical properties of this model: the supercritical series expansions and finite-size exact solutions. With special emphasis we look to the multicritical point and its crossover exponent that characterizes the passage between DP and mean-field critical properties. This crossover occurs in the limit of infinite diffusion rate and our results pointed $ϕ=4$ as the better estimate for the crossover exponent in agreement with computational simulations.

cond-mat.stat-mech↗

arXiv2006

A supercritical series analysis for the generalized contact process with diffusion

We study a model that generalizes the CP with diffusion. An additional transition is included in the model so that at a particular point of its phase diagram a crossover from the directed percolation to the compact directed percolation class will happen. We are particularly interested in the effect of diffusion on the properties of the crossover between the universality classes. To address this point, we develop a supercritical series expansion for the ultimate survival probability and analyse this series using d-log Padé and partial differential approximants. We also obtain approximate solutions in the one- and two-site dynamical mean-field approximations. We find evidences that, at variance to what happens in mean-field approximations, the crossover exponent remains close to $ϕ=2$ even for quite high diffusion rates, and therefore the critical line in the neighborhood of the multicritical point apparently does not reproduce the mean-field result (which leads to $ϕ=0$) as the diffusion rate grows without bound.

cond-mat.stat-mech↗

arXiv2006

A two-variable series for the contact process with diffusion

In this work we use the technique of the partial differential approximants to determine, from a pertubative supercritical series expansion for the ulimate survival probability, the critical line of the contact process model in one dimension with diffusion and estimate the value of the crossover exponent that characterizes the change of the critical behavior from the 1d directed percolation universality class to the mean-field directed percolation universality class. This crossover occurs in the limit of infinite diffusion rate.

cond-mat.stat-mech↗

arXiv2006

Generalized Manna sandpile model with height restrictions

Sandpile models with conserved number of particles (also called fixed energy sandpiles) may undergo phase transitions between active and absorbing states. We generalize the Manna sandpile model with fixed number of particles, introducing a parameter $-1 \leq λ\leq 1$ related to the toppling of particles from active sites to its first neighbors. In particular, we discuss a model with height restrictions, allowing for at most two particles on a site. Sites with double occupancy are active, and their particles may be transfered to first neighbor sites, if the height restriction do allow the change. For $λ=0$ each one of the two particles is independently assigned to one of the two first neighbors and the original stochastic sandpile model is recovered. For $λ=1$ exactly one particle will be placed on each first neighbor and thus a deterministic (BTW) sandpile model is obtained. When $λ=-1$ two particles are moved to one of the first neighbors, and this implies that the density of active sites is conserved in the evolution of the system, and no phase transition is observed. Through simulations of the stationary state, we estimate the critical density of particles and the critical exponents as functions of $λ$.

cond-mat.stat-mech↗

arXiv2005

Study of universality crossover in the contact process

We consider a generalization of the contact process stochastic model, including an additional autocatalitic process. The phase diagram of this model in the proper two-parameter space displays a line of transitions between an active and an absorbing phase which starts at the critical point of the contact process and ends at the transition point of the voter model. Thus, a crossover between the directed percolation and the compact percolation universality classes is observed at this latter point. We study this crossover by a variety of techniques. Using supercritical series expansions analyzed with partial differential approximants, we obtain precise estimates of the crossover behavior of the model. In particular, we find an estimate for the crossover exponent $ϕ=2.00 \pm 0.02$. We also show arguments that support the conjecture $ϕ=2$.

cond-mat.stat-mech↗