arXiv subjects

A. J. F. de Souza

Publications and source records attributed to A. J. F. de Souza.

4 recordsLinked to original sources

arXiv2022

Lyapunov exponent in the Vicsek model

The well-known Vicsek model describes the dynamics of a flock of self-propelled particles (SPPs). Surprisingly, there is no direct measure of the chaotic behavior of such systems. Here, we discuss the dynamical phase transition present in Vicsek systems in light of the largest Lyapunov exponent (LLE), which is numerically computed by following the dynamical evolution in tangent space for up to two million SPPs. As discontinuities in the neighbor weighting factor hinder the computations, we propose a smooth form of the Vicsek model. We find a chaotic regime for the collective behavior of the SPPs based on the LLE. The dependence of LLE with the applied noise, used as a control parameter, changes sensibly in the vicinity of the well-known transition points of the Vicsek model.

cond-mat.stat-mech↗

arXiv2020

Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

We perform short-time Monte Carlo simulations to study the criticality of the isotropic two-state majority-vote model on cubic lattices of volume $N = L^3$, with $L$ up to $2048$. We obtain the precise location of the critical point by examining the scaling properties of a new auxiliary function $Ψ$. We perform finite-time scaling analysis to accurately calculate the whole set of critical exponents, including the dynamical critical exponent $z=2.027(9)$, and the initial slip exponent $θ= 0.1081(1)$. Our results indicate that the majority-vote model in three dimensions belongs to the same universality class of the three-dimensional Ising model.

cond-mat.stat-mech↗

arXiv2000

Effects of disorder and magnetic field in frustrated magnets

In this work a site diluted antiferromagntic Ising model in the FCC lattice is studied by Monte Carlo simulation. At low temperatures, we find that as the external field is increased the transition from the antiferromagnetic phase to the superantiferromagnetic one occurs through an intermediate phase which is not present in the undiluted system. This new phase ordering has three distinct values for the sublattice magnetizations corresponding to one of the phases found in a recent mean field calculation thus suggesting that in strongly frustrated systems many novel spins ordering may arises as found experimentally, for instance, in some pyrochlores.

cond-mat.stat-mech↗

arXiv2000

Critical behavior of the S=1/2 Heisenberg ferromagnet: A Handscomb quantum Monte Carlo study

We investigate the critical relaxational dynamics of the S=1/2 Heisenberg ferromagnet on a simple cubic lattice within the Handscomb prescription on which it is a diagrammatic series expansion of the partition function that is computed by means of a Monte Carlo procedure. Using a phenomenological renormalization group analysis of graph quantities related to the spin susceptibility and order parameter, we obtain precise estimates for the critical exponents relations $γ/ ν= 1.98\pm 0.01 $ and $β/ν= 0.512 \pm 0.002$ and for the Curie temperature $k_BT_c/J = 1.6778 \pm 0.0002$. The critical correlation time of both energy and susceptibility is also computed. We found that the number of Monte Carlo steps needed to generate uncorrelated diagram configurations scales with the system's volume. We estimate the efficiency of the Handscomb method comparing its ability in dealing with the critical slowing down with that of other quantum and classical Monte Carlo prescriptions.

cond-mat.stat-mech↗