J. M. de Araújo

SELF-SIMILAR MAGNETORESISTANCE OF FIBONACCI ULTRATHIN MAGNETIC FILMS

We study numerically the magnetic properties (magnetization and magnetoresistance) of ultrathin magnetic films (Fe/Cr) grown following the Fibonacci sequence. We use a phenomenological model which includes Zeeman, cubic anisotropy, bilinear, and biquadratic exchange energies. Our physical parameters are based on experimental data recently reported, which contain biquadratic exchange coupling with magnitude comparable to the bilinear exchange coupling. When biquadratic exchange coupling is sufficiently large a striking self-similar pattern emerges.

Magnetization in quasiperiodic magnetic multilayers with biquadratic exchange coupling

A theoretical study of the magnetization curves of quasiperiodic magnetic multilayers is presented. We consider structures composed by ferromagnetic films (Fe) with interfilm exchange coupling provided by intervening nonferromagnetic layers (Cr). The theory is based on a realistic phenomenological model, which includes the following contributions to the free magnetic energy: Zeeman, cubic anisotropy, bilinear, and biquadratic exchange energies. The experimental parameters used here are based on experimental data recently reported, which contain sufficiently strong biquadratic exchange coupling.

Effects of random biquadratic couplings in a spin-1 spin-glass model

Abstract:A spin-1 model, appropriated to study the competition between bilinear (JijSiSj) and biquadratic (KijSi2Sj2) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins.

Mean-field solution of the Blume-Capel model under a random crystal field

Abstract In this work we investigate the Blume–Capel model with infinite-range ferromagnetic interactions and under the influence of a quenched disorder – a random crystal field. For a suitable choice of the random crystal field the model displays a wealth of multicritical behavior, continuous and first-order transition lines, as well as re-entrant behavior. The resulting phase diagrams show a variety of topologies as a function of the disorder parameter p . A comparison with recent results on the Blume–Capel model in random crystal field is discussed.

The anisotropic Ashkin–Teller model: a renormalization group study

The two-dimensional ferromagnetic anisotropic Ashkin–Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recovers all the known exact results for the square lattice. The correlation length (νT) and crossover (φ) critical exponents are also calculated. With the only exception of the four-state Potts critical point, the entire phase diagram belongs to the Ising universality class.

The random field Blume-Capel model revisited

Abstract We have revisited the mean-field treatment for the Blume-Capel model under the presence of a discrete random magnetic field as introduced by Kaufman and Kanner (1990). The magnetic field ( H ) versus temperature ( T ) phase diagrams for given values of the crystal field D were recovered in accordance to Kaufman and Kanner original work. However, our main goal in the present work was to investigate the distinct structures of the crystal field versus temperature phase diagrams as the random magnetic field is varied because similar models have presented reentrant phenomenon due to randomness. Following previous works we have classified the distinct phase diagrams according to five different topologies. The topological structure of the phase diagrams is maintained for both H - T and D - T cases. Although the phase diagrams exhibit a richness of multicritical phenomena we did not found any reentrant effect as have been seen in similar models.

Superdiffusion driven by exponentially decaying memory

A superdiffusive random walk model with exponentially decaying memory is reported. This seems to be a self-contradictory statement, since it is well known that random walks with exponentially decaying temporal correlations can be approximated arbitrarily well by Markov processes and that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. The solution to the apparent paradox is that the model is genuinely non-Markovian, due to a time-dependent decay constant associated with the exponential behavior.

First-order transitions and triple point on a random p-spin interaction model

The effects of competing quadrupolar- and spin-glass orderings are investigated on a spin-1 Ising model with infinite-range random p -spin interactions. The model is studied through the replica approach and a phase diagram is obtained in the limit p . The phase diagram, obtained within replica-symmetry breaking, exhibits a very unusual feature in magnetic models: three first-order transition lines meeting at a common triple point, where all phases of the model coexist.

Zero-temperature TAP equations for the Ghatak-Sherrington model

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field D for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of D.Abstract:The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field D for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of D.

Multifractality signatures in quasars time series – I. 3C 273

The presence of multifractality in a time series shows different correlations for different timescales as well as intermittent behaviour that cannot be captured by a single scaling exponent. The identification of a multifractal nature allows for a characterization of the dynamics and of the intermittency of the fluctuations in non-linear and complex systems. In this study, we search for a possible multifractal structure (multifractality signature) of the flux variability in the quasar 3C 273 time series for all electromagnetic wavebands at different observation points, and the origins for the observed multifractality. This study is intended to highlight how the scaling behaves across the different bands of the selected candidate, which can be used as an additional new technique to group quasars based on the fractal signature observed in their time series and determine whether quasars are non-linear physical systems or not. The multifractal detrended moving average algorithm (MFDMA) has been used to study the scaling in non-linear, complex, and dynamic systems. To achieve this goal, we applied the backward (θ = 0) MFDMA method for one-dimensional signals. We observe weak multifractal (close to monofractal) behaviour in some of the time series of our candidate except in the mm, UV and X-ray bands. The non-linear temporal correlation is the main source of the observed multifractality in the time series whereas the heaviness of the distribution contributes less.