André P. Vieira

Phase diagram of a random-anisotropy mixed-spin Ising model

We investigate the phase diagram of a mixed spin-1/2--spin-1 Ising system in the presence of quenched disordered anisotropy. We carry out a mean-field and a standard self-consistent Bethe--Peierls calculation. Depending on the amount of disorder, there appear novel transition lines and multicritical points. Also, we report some connections with a percolation problem and an exact result in one dimension.

Protecting Clean Critical Points by Local Disorder Correlations

We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics.

Correlation amplitude and entanglement entropy in random spin chains

Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1/2 chain focusing on the long-length and ground-state behavior of the average time-independent spin-spin correlation function C(l)=upsilon l(-eta). In addition to the well-known universal (disorder-independent) power-law exponent eta=2, we find interesting universal features displayed by the prefactor upsilon=upsilon(o)/3, if l is odd, and upsilon=upsilon(e)/3, otherwise. Although upsilon(o) and upsilon(e) are nonuniversal (disorder dependent) and distinct in magnitude, the combination upsilon(o)+upsilon(e)=-1/4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.

Dynamics of snoring sounds and its connection with obstructive sleep apnea

Snoring is extremely common in the general population and when irregular may indicate the presence of obstructive sleep apnea. We analyze the overnight sequence of wave packets — the snore sound — recorded during full polysomnography in patients referred to the Sleep Laboratory due to suspected obstructive sleep apnea. We hypothesize that irregular snore, with duration in the range between 10 and 100 s, correlates with respiratory obstructive events. We find that the number of irregular snores — easily accessible, and quantified by what we call the snore time interval index (STII) — is in good agreement with the well-known apnea–hypopnea index, which expresses the severity of obstructive sleep apnea and is extracted only from polysomnography. In addition, the Hurst analysis of the snore sound itself, which calculates the fluctuations in the signal as a function of time interval, is used to build a classifier that is able to distinguish between patients with no or mild apnea and patients with moderate or severe apnea.

Aperiodic quantum XXZ chains: Renormalization-group results

We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly-known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures, and their comparison with the random-singlet phase, characteristic of random-bond chains.

Fluctuation analyses for pattern classification in nondestructive materials inspection

We review recent work on the application of fluctuation analyses of time series for pattern classification in nondestructive materials inspection. These analyses are based on the evaluation of time-series fluctuations across time intervals of increasing size, and were originally introduced in the study of fractals. A number of examples indicate that this approach yields relevant features allowing the successful classification of patterns such as (i) microstructure signatures in cast irons, as probed by backscattered ultrasonic signals; (ii) welding defects in metals, as probed by TOFD ultrasonic signals; (iii) gear faults, based on vibration signals; (iv) weld-transfer modes, as probed by voltage and current time series; (v) microstructural composition in stainless steel, as probed by magnetic Barkhausen noise and magnetic flux signals.

Analytical approach to directed sandpile models on the Apollonian network

We investigate a set of directed sandpile models on the Apollonian network, which are inspired by the work of Dhar and Ramaswamy [Phys. Rev. Lett. 63, 1659 (1989)] on Euclidian lattices. They are characterized by a single parameter q , which restricts the number of neighbors receiving grains from a toppling node. Due to the geometry of the network, two- and three-point correlation functions are amenable to exact treatment, leading to analytical results for avalanche distributions in the limit of an infinite system for q=1,2 . The exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite-size systems when larger values of q are considered. Finally, a detailed description of the local flux properties is provided by a multifractal scaling analysis.

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice.

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings

We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is verified for random spin-1 chains, we show that different adaptations of the SDRG scheme may lead to different qualitative conclusions about the nature of the ground state in the presence of aperiodic coupling modulations.

Correlated disordered interactions on Potts models

Using a weak-disorder scheme and real-space renormalization-group techniques, we obtain analytical results for the critical behavior of various q-state Potts models with correlated disordered exchange interactions along d(1) of d spatial dimensions on hierarchical (Migdal-Kadanoff) lattices. Our results indicate qualitative differences between the cases d-d(1)=1 (for which we find non-physical random fixed points, suggesting the existence of non-perturbative fixed distributions) and d-d(1)>1 (for which we do find acceptable perturbative random fixed points), in agreement with previous numerical calculations by Andelman and Aharony [Phys. Rev. B 31, 4305 (1985)]. We also rederive a criterion for relevance of correlated disorder, which generalizes the usual Harris criterion.