Two-dimensional Compass Research Articles

As camadas de intertextualidade das XIV Variações sobre o tema de Xangô de Almeida Prado

A existência da obra XIV Variações sobre o tema de Xangô, de Almeida Prado, em duas versões (uma de 1961, para piano, e outra de 1998, para fagote e piano), e o depoimento do compositor de que cada variação se refere a um gênero do folclore brasileiro criam um cenário complexo de intertextualidade. Primeiramente, o artigo traz uma contextualização da obra nacionalista, obra esta que segue as instruções de Mário de Andrade e Mozart Camargo Guarnieri. Em seguida são abordados conceitos de intertextualidade que importam neste recorte de trabalho, entre outros, a bússola intertextual de Gabriel de Mesquita, e representamos em gráfico as quatro camadas de intertextualidade encontradas nessa obra. Durante a abordagem destas camadas, damos um enfoque na relação da variação IV com sua referência externa, o Ponteio n. 45 de Guarnieri. A análise comparativa dos dois intertextos, tanto nos seus parâmetros superficiais quanto profundos, mostra que eles se relacionam através de modelagem de perfil. A comparação das duas versões, escritas com uma distância de 37 anos, evidencia como a nova versão, mesmo mantendo o piano inalterado, ambienta a obra na fase pós-moderna do compositor. Por último, compilamos as tipologias de intertextualidade dentro da bússola intertextual e propomos uma reformulação da bússola bidimensional e sua ampliação para três dimensões, no intuito de incorporar nesta um novo conceito, a metaintertextualidade, a partir da relação sugerida pelas duas versões das XIV Variações de Almeida Prado.

Local broken symmetry and spin conductivity in the two-dimensional model in the compass lattice

The spin transport in the neighborhood of a quantum phase transition in the two-dimensional compass model is studied. The model presents Heisenberg compass interactions of amplitudes Jx and Jz and next and next-nearest neighbor Heisenberg interactions J1 and J2. Where the Heisenberg interactions are isotropic in spin space, but the compass interactions depending on the bond direction. Our results show a conductivity varying a little with the behavior of critical parameters η = J2∕J1, Jz and Jx. Hence, we obtain a little variation of the phase transition to magnetically ordered phase on conductivity. Besides, we obtain a conventional conductor behavior for the AC spin transport in the limit ω → 0 or DC limit.

High-temperature dynamics in quantum compass models

We analyze the high temperature spin dynamics of compass models using a moment expansion. We point out that the evaluation of moments maps to the enumeration of paths in a branching process on the lattice. This mapping to a statistical mechanics combinatorics problem provides an elegant visualization of the analysis. We present results for the time dependent spin correlation function (which is of relevance to NMR experiments) for two compass models: the Kitaev honeycomb model and two-dimensional compass model.

One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization

We introduce a one-dimensional (1D) pseudospin model on a ladder where the Ising interactions along the legs and along the rungs alternate between $X_{i}X_{i+1}$ and $Z_{i}Z_{i+1}$ for even/odd bond (rung). We include also the next nearest neighbor Ising interactions on plaquettes' diagonals that alternate in such a way that a model where only leg interactions are switched on is equivalent to the one when only the diagonal ones are present. Thus in the absence of rung interactions the model can interpolate between two 1D compass models. The model posses local symmetries which are the parities within each $2\times 2$ cell (plaquette) of the ladder. We find that for different values of the interaction it can realize ground states that differ by the patterns formed by these local parities. By exact diagonalization we derive detailed phase diagrams for small systems of $L=4$, 6 and 8 plaquettes, and use next $L=12$ to identify generic phases that appear in larger systems as well. Among them we find a nematic phase with macroscopic degeneracy when the leg and diagonal interactions are equal and the rung interactions are larger than a critical value. The nematic phase is similar to the one found in the two-dimensional compass model. For particular parameters the low-energy sector of the present plaquette model reduces to a 1D compass model with spins $S=1$ which suggests that it realizes peculiar crossovers within the class of compass models. Finally, we show that the model can realize phases with broken translation invariance which can be either dimerized, trimerized, \textit{etcetera}, or completely disordered and highly entangled in a~well identified window of the phase diagram.

One-dimensional AGMI sensor with Co66Fe4Si15B15 ribbon as sensing element

A novel asymmetric giant magneto impedance (AGMI) sensor was developed and the performance of the sensor was carefully studied. This one dimensional sensor can be further developed as a two-dimensional compass that can be used for navigational purposes. We used commercial Metglas 2714A ribbon. The sensor uses Co66Fe4Si15B15 ribbon as a sensing element.

Directional Ordering of Fluctuations in a Two-Dimensional Compass Model

In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in orbital space and in real space. We discuss a classical realization of directional coupling in two dimensions. Despite extensive degeneracy of the ground state, the model exhibits partial orbital ordering in the form of directional ordering of fluctuations at low temperatures stabilized by an entropy gap. Transition to the disordered phase is shown to be in the Ising universality class through exact mapping and multicanonical Monte Carlo simulations.

Three-dimensional odor compass

A three-dimensional odor compass is proposed to develop a navigation tool used in searching for an odor source. The compass, which continuously points to the source, is equipped with four semiconductor gas sensors and a small fan to draw air to the sensors. The direction of the source is obtained by rotating the compass head to obtain the direction where the responses of the sensors along the horizontal and vertical directions are balanced. The following algorithmic improvements have been made to reduce the measurement time after the previous report on the two-dimensional compass. First, the transient sensor response model is introduced to compensate the response delay of the gas sensors. Secondly, the head of the compass is made to rotate continuously and three-dimensionally during the directional estimation to gather plenty of data over a short time period. As a result, the measurement time at a practical level (20 s) has been achieved. The experimental results demonstrate the effectiveness of the compass in practical environments where the wind blows three-dimensionally and/or where the odor distribution is modified by an obstacle.