arXiv subjects

L. H. Miranda-Filho

Publications and source records attributed to L. H. Miranda-Filho.

3 recordsLinked to original sources

arXiv2026

Evidence of the de Almeida-Thouless transition in three-dimensional spin glasses

The nature of spin-glass states in a magnetic field remains a major open problem in statistical physics. The existence of the de Almeida-Thouless (dAT) transition for three-dimensional (3D) spin glasses in a field is still debated. We introduce a new computational method to define the spin-glass susceptibility, which is robust against the broad tail in the overlap distribution that undermines conventional analyses. Applying this approach to the Edwards-Anderson spin-glass model in 2D and 3D, and contrasting with the 3D Ising (without disorder) and mean-field spin-glass models, we find a stark difference: the locus of susceptibility maxima bends to the right in the field-temperature plane for the Ising and 2D spin-glass cases, indicating a supercritical crossover line, but bends to the left for the mean-field and 3D spin glasses - a signature of the dAT line. Finite-size scaling further suggests that the peak susceptibility diverges with system size in 3D spin glasses under a field, while saturating in 2D. These results provide direct numerical evidence for the dAT transition in 3D, supporting the replica symmetry breaking scenario.

cond-mat.stat-mech↗

arXiv2023

On the probability distributions of the force and potential energy for a system with an infinite number of random point sources

In this work, we study the probability distribution for the force and potential energy of a test particle interacting with $N$ point random sources in the limit $N\rightarrow\infty$. The interaction is given by a central potential $V(R)=k/R^{δ-1}$ in a $ d$-dimensional euclidean space, where $R$ is the random relative distance between the source and the test particle, $δ$ is the force exponent, and $k$ is the coupling parameter. In order to assure a well-defined limit for the probability distribution of the force and potential energy, we { must} renormalize the coupling parameter and/or the system size as a function of the number $N$ of sources. We show the existence of three non-singular limits, depending on the exponent $δ$ and the spatial dimension $d$. (i) For $δ d+1$ the potential energy converges to a random variable and the force to a random vector. This limit is called Thermodynamic Limit. (iii) For $d<δ<d+1$ the potential energy converges to its mean and the force to a random vector. This limit is called Mixed Limit Also, we show the existence of two singular limits: (iv) for $δ=d$ the potential energy converges to its mean and the force to zero, and (v) for $δ=d+1$ the energy converges to a finite value and the force to a random vector.

math-ph↗

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↗