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.Comment: v1: 16 pages, 15 figures; v2: 17 pages, improved discussions and statistics, references added, published versio

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.Comment: Minor corrections; published versio

Mean-field model for a mixture of biaxial nematogens and dipolar nanoparticles

We analyze a mean-field model for mixtures involving biaxial nematogens and dipolar nanoparticles, taking into account orientational and isotropic pair interactions between nematogens, but also orientational nematogen-nanoparticle interactions. We determine bulk equilibrium phase diagrams for a wide range of interaction strengths, identifying in each case the effect of the nanoparticles on the stability of nematic phases and on the appearance of multicritical points. Special attention is given to the limit of low concentration of nanoparticles, in which their effect on the temperatures of both the first-order uniaxial-isotropic and the continuous biaxial-uniaxial transitions is investigated in detail

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 on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659 (1989)) for Euclidian lattices. They are characterized by a single parameter $q$, that 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 the 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.Comment: 7 pages in two-column format, 10 illustrations, 5 figure

Microstructure identification via detrended fluctuation analysis of ultrasound signals

We describe an algorithm for simulating ultrasound propagation in random one-dimensional media, mimicking different microstructures by choosing physical properties such as domain sizes and mass densities from probability distributions. By combining a detrended fluctuation analysis (DFA) of the simulated ultrasound signals with tools from the pattern-recognition literature, we build a Gaussian classifier which is able to associate each ultrasound signal with its corresponding microstructure with a very high success rate. Furthermore, we also show that DFA data can be used to train a multilayer perceptron which estimates numerical values of physical properties associated with distinct microstructures.Comment: Submitted to Phys. Rev.

Experimental Study of Two Impinging Jets Aligned With a Crossflow

Laser Doppler measurements provide information on the flowfield created by twin impinging jets aligned with a low velocity crossflow. The experiments were carried out for a Reynolds number based on the jet exit conditions of Rej = 4.3 × 104, an impingement height of 20.1 jet diameters and for a velocity ratio between the jet exit and the crossflow VR = Vj/Uo of 22.5, and an inter-jet spacing of S = 6D. The results show a large penetration of the first (upstream) jet that is deflected by the crossflow and impinges on the ground, giving rise to a ground vortex due to the collision of the radial wall and the crossflow that wraps around the impinging point like a scarf. The second jet (located downstream) is not so affected by the crossflow in terms of deflection, but due to the downstream wall jet that flows radially from the impinging point of the first jet it does not reach the ground. The results indicate a new flow pattern not yet reported so far, that is most relevant for a VSTOL aircraft operating in ground vicinity with front wind or small forward movement may result in enhanced under pressures in the aft part of the aircraft causing a suction down force and a change of the pitching moment towards the ground.Fundação para a Ciência e a Tecnologiainfo:eu-repo/semantics/publishedVersio

Fatigue in disordered media

We obtain the Paris law of fatigue crack propagation in a disordered solid using a fuse network model where the accumulated damage in each resistor increases with time as a power law of the local current amplitude. When a resistor reaches its fatigue threshold, it burns irreversibly. Over time, this drives cracks to grow until the system is fractured in two parts. We study the relation between the macroscopic exponent of the crack growth rate -- entering the phenomenological Paris law -- and the microscopic damage-accumulation exponent, $\gamma$, under the influence of disorder. The way the jumps of the growing crack, $\Delta a$, and the waiting-time between successive breaks, $\Delta t$, depend on the type of material, via $\gamma$, are also investigated. We find that the averages of these quantities, and $/$, scale as power laws of the crack length $a$, $ \propto a^{\alpha}$ and $/ \propto a^{-\beta}$, where is the average rupture time. Strikingly, our results show, for small values of $\gamma$, a decrease in the exponent of the Paris law in comparison with the homogeneous case, leading to an increase in the lifetime of breaking materials. For the particular case of $\gamma=0$, when fatigue is exclusively ruled by disorder, an analytical treatment confirms the results obtained by simulation