Phase space solutions in scalar-tensor cosmological models

An analysis of the solutions for the field equations of generalized scalar-tensor theories of gravitation is performed through the study of the geometry of the phase space and the stability of the solutions, with special interest in the Brans-Dicke model. Particularly, we believe to be possible to find suitable forms of the Brans-Dicke parameter omega and potential V of the scalar field, using the dynamical systems approach, in such a way that they can be fitted in the present observed scenario of the Universe.Comment: revtex, 2 pages, 4 eps figures, to appear in Brazilian Journal of Physics (proceedings of the Conference 100 Years of Relativity, Sao Paulo, Brazil, August 2005

A note on the infrared behavior of the compactified Ginzburg--Landau model in a magnetic field

We consider the Euclidean large-$N$ Ginzburg--Landau model in $D$ dimensions, $d$ ($d\leq D$) of them being compactified. For D=3, the system can be supposed to describe, in the cases of d=1, d=2, and d=3, respectively, a superconducting material in the form of a film, of an infinitely long wire having a rectangular cross-section and of a brick-shaped grain. We investigate the fixed-point structure of the model, in the presence of an external magnetic field. An infrared-stable fixed points is found, which is independent of the number of compactified dimensions. This generalizes previous work for type-II superconducting filmsComment: LATEX, 6 pages no figures. arXiv admin note: 80% of text overlaps with arXiv:1102.139

Correlated electrons systems on the Apollonian network

Strongly correlated electrons on an Apollonian network are studied using the Hubbard model. Ground-state and thermodynamic properties, including specific heat, magnetic susceptibility, spin-spin correlation function, double occupancy and one-electron transfer, are evaluated applying direct diagonalization and quantum Monte Carlo. The results support several types of magnetic behavior. In the strong-coupling limit, the quantum anisotropic spin 1/2 Heisenberg model is used and the phase diagram is discussed using the renormalization group method. For ferromagnetic coupling, we always observe the existence of long-range order. For antiferromagnetic coupling, we find a paramagnetic phase for all finite temperatures.Comment: 7 pages, 8 figure