Fases e criticalidade no modelo ashkin - teller de três cores

The usual Ashkin-Teller (AT) model is obtained as a superposition of two Ising models coupled through a four-spin interaction term. In two dimension the AT model displays a line of fixed points along which the exponents vary continuously. On this line the model becomes soluble via a mapping onto the Baxter model. Such richness of multicritical behavior led Grest and Widom to introduce the N-color Ashkin-Teller model (N-AT). Those authors made an extensive analysis of the model thus introduced both in the isotropic as well as in the anisotropic cases by several analytical and computational methods. In the present work we define a more general version of the 3-color Ashkin-Teller model by introducing a 6-spin interaction term. We investigate the corresponding symmetry structure presented by our model in conjunction with an analysis of possible phase diagrams obtained by real space renormalization group techniques. The phase diagram are obtained at finite temperature in the region where the ferromagnetic behavior is predominant. Through the use of the transmissivities concepts we obtain the recursion relations in some periodical as well as aperiodic hierarchical lattices. In a first analysis we initially consider the two-color Ashkin-Teller model in order to obtain some results with could be used as a guide to our main purpose. In the anisotropic case the model was previously studied on the Wheatstone bridge by Claudionor Bezerra in his Master Degree dissertation. By using more appropriated computational resources we obtained isomorphic critical surfaces described in Bezerra's work but not properly identified. Besides, we also analyzed the isotropic version in an aperiodic hierarchical lattice, and we showed how the geometric fluctuations are affected by such aperiodicity and its consequences in the corresponding critical behavior. Those analysis were carried out by the use of appropriated definitions of transmissivities. Finally, we considered the modified 3-AT model with a 6-spin couplings. With the inclusion of such term the model becomes more attractive from the symmetry point of view. For some hierarchical lattices we derived general recursion relations in the anisotropic version of the model (3-AAT), from which case we can obtain the corresponding equations for the isotropic version (3-IAT). The 3-IAT was studied extensively in the whole region where the ferromagnetic couplings are dominant. The fixed points and the respective critical exponents were determined. By analyzing the attraction basins of such fixed points we were able to find the three-parameter phase diagram (temperature £ 4-spin coupling £ 6-spin coupling). We could identify fixed points corresponding to the universality class of Ising and 4- and 8-state Potts model. We also obtained a fixed point which seems to be a sort of reminiscence of a 6-state Potts fixed point as well as a possible indication of the existence of a Baxter line. Some unstable fixed points which do not belong to any aforementioned q-state Potts universality class was also found

Ondas de spin em super-redes ferromagnéticas com campo de anisotropia

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Espectro das ondas de spin lineares e não-lineares em multicamadas magnéticas anisotrópicas

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Ondas de spin em nanofilmes nagnéticos acoplados quasiperiodicamente

We studied the spin waves modes that can propagate in magnetic multilayers composed of ferromagnetic metallic films in the nanometer scale. The ferromagnetic films (iron) are separated and coupled through the nonmagnetic spacer films (chromium). The films that make up the multilayer are stacked in a quasiperiodic pattern, following the Fibonacci and double period sequences. We used a phenomenological theory taking into account: the Zeeman energy (between the ferromagnetic films and the external magnetic field), the energy of the magneto-crystalline anisotropy (present in the ferromagnetic films), the energy of the bilinear and biquadratic couplings (between the ferromagnetic films) and the energy of the dipole-dipole interaction (between the ferromagnetic films), to describe the system. The total magnetic energy of the system is numerically minimized and the equilibrium angles of the magnetization of each ferromagnetic film are determined. We solved the equation of motion of the multilayer to find the dispersion relation for the system and, as a consequence, the spin waves modes frequencies. Our theoretical results show that, in the case of trilayers (Fe/Cr/Fe), our model reproduces with excellent agreement experimental results of Brillouin light scattering, known from the literature, by adjusting the physical parameters of the nanofilms. Furthermore, we generalize the model to N ferromagnetic layers which allowed us to determine how complex these systems become when we increase the number of components. It is worth noting that our theoretical calculations generalize all the results known from the literature

Ondas de spin em quasi-cristais magnônicos

In this paper we investigate the spectra of band structures and transmittance in magnonic quasicrystals that exhibit the so-called deterministic disorders, specifically, magnetic multilayer systems, which are built obeying to the generalized Fibonacci (only golden mean (GM), silver mean (SM), bronze mean (BM), copper mean (CM) and nickel mean (NM) cases) and k-component Fibonacci substitutional sequences. The theoretical model is based on the Heisenberg Hamiltonian in the exchange regime, together with the powerful transfer matrix method, and taking into account the RPA approximation. The magnetic materials considered are simple cubic ferromagnets. Our main interest in this study is to investigate the effects of quasiperiodicity on the physical properties of the systems mentioned by analyzing the behavior of spin wave propagation through the dispersion and transmission spectra of these structures. Among of these results we detach: (i) the fragmentation of the bulk bands, which in the limit of high generations, become a Cantor set, and the presence of the mig-gap frequency in the spin waves transmission, for generalized Fibonacci sequence, and (ii) the strong dependence of the magnonic band gap with respect to the parameters k, which determines the amount of different magnetic materials are present in quasicrystal, and n, which is the generation number of the sequence k-component Fibonacci. In this last case, we have verified that the system presents a magnonic band gap, whose width and frequency region can be controlled by varying k and n. In the exchange regime, the spin waves propagate with frequency of the order of a few tens of terahertz (THz). Therefore, from a experimental and technological point of view, the magnonic quasicrystals can be used as carriers or processors of informations, and the magnon (the quantum spin wave) is responsible for this transport and processing

Controle de posição com restrição à orientação de um Veículo Aéreo Não-Tripulado tipo Quadrirrotor

Quadrotors aircraft are composed by four propellers mounted on four engines on a cross or x disposition, and, in this structure, the engines on the same arm spin in the same direction and the other arm in the opposite direction. By rotating each helix generates vertical upward thrust. The control is done by varying the rotational speed of each motor. Among the advantages of this type of vehicle can cite the mechanical simplicity of construction, the high degree of maneuverability and the ability to have vertical takeoffs and landings. The modeling and control of quadrirrotores have been a challenge due to problems such as nonlinearity and coupling between variables. Several strategies have been developed to control this type of vehicle, from the classical control to modern. There are air surveillance applications where a camera is fixed on the vehicle to point forward, where it is desired that the quadrotor moves at a fixed altitude toward the target also pointing forward, which imposes an artificial constraint motion, because it is not desired that it moves laterally, but only forwards or backwards and around its axes . This restriction is similar to the naturally existing on robots powered by wheels with differential drive, which also can not move laterally, due to the friction of the wheels. Therefore, a position control strategy similar to that used in this type of robot could be adapted for aerial robots like quadrotor. This dissertation presents and discusses some strategies for the control of position and orientation of quadrotors found in the literature and proposes a strategy based on dynamic control of mobile robots with differential drive, called the variable reference control. The validity of the proposed strategy is demonstrated through computer simulations

Efeitos de acoplamentos biquadráticos e campos aleatórios em vidros de spins

In this work we have studied the effects of random biquadratic and random fields in spin-glass models using the replica method. The effect of a random biquadratic coupling was studied in two spin-1 spin-glass models: in one case the interactions occur between pairs of spins, whereas in the second one the interactions occur between p spins and the limit p > oo is considered. Both couplings (spin glass and biquadratic) have zero-mean Gaussian probability distributions. In the first model, the replica-symmetric assumption reveals that the system presents two pha¬ses, 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 cou¬plings between the spins. For the case p oo, the replica-symmetric assumption yields again only two phases, namely, paramagnetic and quadrupolar. In both these phases the spin-glass parameter is zero. Besides, it is shown that they are stable under the Almeida-Thouless stability analysis. One of them presents negative entropy at low temperatures. We developed one step of replica simmetry breaking and noticed that a new phase, the biquadratic glass phase, emerge. In this way we have obtained the correct phase diagram, with.three first-order transition lines. These lines merges in a common triple point. The effects of random fields were studied in the Sherrington-Kirkpatrick model consi¬dered in the presence of an external random magnetic field following a trimodal distribu¬tion {P{hi) = p+S(hi - h0) +Po${hi) +pS(hi + h0))- It is shown that the border of the ferromagnetic phase may present, for conveniently chosen values of p0 and hQ, first-order phase transitions, as well as tricritical points at finite temperatures. It is verified that the first-order phase transitions are directly related to the dilution in the fields: the extensions of these transitions are reduced for increasing values of po- In fact, the threshold value pg, above which all phase transitions are continuous, is calculated analytically. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified

Propriedades estáticas e dinâmicas de multicamadas magnéticas acopladas quasiperiodicamente

In this work we study, for two different growth directions, multilayers of nanometric magnetic metallic lms grown, using Fibonacci sequences, in such a way that the thickness of the non-magnetic spacer may vary from a pair of lms to another. We applied a phenomenological theory that uses the magnetic energy to describe the behavior of the system. After we found numerically the global minimum of the total energy, we used the equilibrium angles to obtain magnetization and magnetoresistance curves. Next, we solved the equation of motion of the multilayers to nd the dispersion relation for the system. The results show that, when spacers are used with thickness so that the biquadratic coupling is strong in comparison to the bilinear one, non usual behaviors for both magnetization and magnetoresistance are observed. For example, a dependence on the parity of the Fibonacci generation utilized for constructing the system, a low magnetoresistance step in low external magnetic fields and regions that show high sensibility to small variations of the applied field. Those behaviors are not present in quasiperiodic magnetic multilayers with constant spacer thickness