Propriedades críticas do modelo z(4) em sistemas bi e tridimensionais

A real space renormalization group method is used to investigate the criticality (phase diagrams, critical expoentes and universality classes) of Z(4) model in two and three dimensions. The values of the interaction parameters are chosen in such a way as to cover the complete phase diagrams of the model, which presents the following phases: (i) Paramagnetic (P); (ii) Ferromagnetic (F); (iii) Antiferromagnetic (AF); (iv) Intermediate Ferromagnetic (IF) and Intermediate Antiferromagnetic (IAF). In the hierarquical lattices, generated by renormalization the phase diagrams are exact. It is also possible to obtain approximated results for square and simple cubic lattices. In the bidimensional case a self-dual lattice is used and the resulting phase diagram reproduces all the exact results known for the square lattice. The Migdal-Kadanoff transformation is applied to the three dimensional case and the additional phases previously suggested by Ditzian et al, are not found

Cúbicas galoisianas

Pós-graduação em Matemática - IBILCE

Critical behavior of one-particle spectral weights in the transverse Ising model

We investigate the critical behavior of the spectral weight of a single quasiparticle, one of the key observables in experiment, for the particular case of the transverse Ising model. Series expansions are calculated for the linear chain and the square and simple cubic lattices. For the chain model, a conjectured exact result is discovered. For the square and simple cubic lattices, series analyses are used to estimate the critical exponents. The results agree with the general predictions of Sachdev [Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999)].

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Cation-oxygen interaction and oxygen stability in CaCu3Ti4O12 and CdCu3Ti4O12 lattices

The cubic perovskite related material CaCu3Ti4O12 has attracted a great deal of attention due to the high values of the static dielectric constant, of order 104, approximately constant in the temperature range 100-600 K. The substitution of Ca by Cd results in a similar temperature dependence but a static dielectric constant more than one order of magnitude lower. A theoretical electronic structure study is performed on CaCu3Ti4O12 (CCTO) and CdCu3Ti4O12 (CdCTO) using a tight binding with overlap method. Although the calculations are performed in a paramagnetic configuration, excellent agreement with experiment was found for the calculated band gap of CCTO. In spite of the fact that the band structures of both systems look practically the same, a significant difference is found in the calculated bond strength of Ca-O and Cd-O pairs, driven by the presence of Ti, with Ca-O interaction in CCTO loosened with respect to Cd-O interaction in the cadmium compound. It is suggested that O vacancies are more easily formed in CCTO, this being related to the lower electronegativity of Ca as compared to Cd. The formation of oxygen vacancies could be the origin of the difference in the static dielectric constant of the two compounds.

Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

High-temperature X-ray powder diffraction study of the tetragonal-cubic phase transition in nanocrystalline, compositionally homogeneous ZrO2-CeO2 solid solutions

Crystal structure of compositionally homogeneous, nanocrystalline ZrO2-CeO2 solutions was investigated by X-ray powder diffraction as a function of temperature for compositions between 50 and 65 mol % CeO2 center dot ZrO2-50 and 60 mol % CeO2 solid solutions, which exhibit the t'-form of the tetragonal phase at room temperature, transform into the cubic phase in two steps: t'-to-t '' followed by t ''-to-cubic. But the ZrO2-65 mol % CeO2, which exhibits the t ''-form, transforms directly to the cubic phase. The results suggest that t'-to-t '' transition is of first order, but t ''-to-cubic seems to be of second order. (C) 2008 International Centre for Diffraction Data.

Synchrotron X-ray powder diffraction study of the tetragonal-cubic phase transition in nanostructured ZrO2-Sc2O3 solid solutions

The transition between tetragonal and cubic phases in nanostructured ZrO2-Sc2O3 solid solutions by high-temperature X-ray powder diffraction using synchrotron radiation is presented. ZrO2-8 and 11 mol% Sc2O3 nanopowders that exhibit the t'- and t ''-forms of the tetragonal phase, respectively, were synthesized by a stoichiometric nitrate-lysine gel-combustion route. The average crystallite size treated at 900 degrees C was about 25 nm for both compositions. Our results showed that t'-t '' and t ''-cubic transitions take place for the 8 and 11 mol% Sc2O3 samples, respectively. (C) 2008 International Centre for Diffraction Data.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Mn-doped cubic BN as an atomiclike memory device: A density functional study

We investigate the electronic properties of Mn(B) substitutional doping in cubic boron nitride (BN), for different charge states, using density functional theory (DFT) calculations. We show that the neutral Mn has a nonmagnetic ground state (S=0). Upon charge injection, it is unambiguously shown that the Mn(B)(-) has a high-spin configuration with a strong, localized magnetic moment of 5 mu(Bohr). We developed a simple model, parameterized by the DFT results, that allows us to interpret the rules played by the crystal-field and exchange-correlation splitting in the magnetization process.

Transition-metal 13-atom clusters assessed with solid and surface-biased functionals

First-principles density-functional theory studies have reported open structures based on the formation of double simple-cubic (DSC) arrangements for Ru(13), Rh(13), Os(13), and Ir(13), which can be considered an unexpected result as those elements crystallize in compact bulk structures such as the face-centered cubic and hexagonal close-packed lattices. In this work, we investigated with the projected augmented wave method the dependence of the lowest-energy structure on the local and semilocal exchange-correlation (xc) energy functionals employed in density-functional theory. We found that the local-density approximation (LDA) and generalized-gradient formulations with different treatment of the electronic inhomogeneities (PBE, PBEsol, and AM05) confirm the DSC configuration as the lowest-energy structure for the studied TM(13) clusters. A good agreement in the relative total energies are obtained even for structures with small energy differences, e. g., 0.10 eV. The employed xc functionals yield the same total magnetic moment for a given structure, i.e., the differences in the bond lengths do not affect the moments, which can be attributed to the atomic character of those clusters. Thus, at least for those systems, the differences among the LDA, PBE, PBEsol, and AM05 functionals are not large enough to yield qualitatively different results. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3577999]

Low dimensional behavior in three-dimensional coupled map lattices

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows 1/f noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension. (c) 2008 Elsevier Ltd. All rights reserved.