Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory

Green's functions are a central element in the attempt to understand non-perturbative phenomena in Yang-Mills theory. Besides the propagators, 3-point Green's functions play a significant role, since they permit access to the running coupling constant and are an important input in functional methods. Here we present numerical results for the two non-vanishing 3-point Green's functions in 3d pure SU(2) Yang-Mills theory in (minimal) Landau gauge, i.e. the three-gluon vertex and the ghost-gluon vertex, considering various kinematical regimes. In this exploratory investigation the lattice volumes are limited to 20^3 and 30^3 at beta=4.2 and beta=6.0. We also present results for the gluon and the ghost propagators, as well as for the eigenvalue spectrum of the Faddeev-Popov operator. Finally, we compare two different numerical methods for the evaluation of the inverse of the Faddeev-Popov matrix, the point-source and the plane-wave-source methods.Comment: 18 pages, 12 figures, 3 table

Preferential attachment of communities: the same principle, but a higher level

The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules or clusters), and the links refer to members shared by two communities. Our analysis indicates that the development of this modular structure is driven by preferential attachment, in complete analogy with the growth of the underlying network of nodes. We study how the links between communities are born in a growing co-authorship network, and introduce a simple model for the dynamics of overlapping communities.Comment: 7 pages, 3 figure

Structural and dielectric properties of laser ablated BaTiO3 films deposited over electrophoretically dispersed CoFe2O4 grains

Thin film nanocomposites with mixed connectivity, composed by CoFe2O4 grains deposited by electrophoresis on Si|Pt substrates and subsequently covered by a laser ablation deposited BaTiO3 layer were prepared with different cobalt ferrite concentrations. Their structure presented a combination of BaTiO3, with its tetragonal and the orthorhombic phases coexisting at room temperature, and CoFe2O4 with the cubic spinel structure. The cobalt ferrite nanograins were under in-plane tensile stress, while the BaTiO3 phase was under in-plane compressive stress. The dielectric measurements showed that as the barium titanate grain size decreased, its ferroelectric Curie temperature shifted to lower temperatures relative to the bulk. This grain size dependent TC shift was associated and modeled by a core-shell structure of BaTiO3 grains in the films, with a tetragonal core and cubic shell. Additionally a diffuse tetragonal-orthorhombic phase transition was observed and, in agreement with Raman spectroscopy results, associated to the coexistence of barium titanate orthorhombic and tetragonal phases in the room temperature region. This led to the formation of polar nanoclusters with random polarization orientations, which induced a frustrated phase transition between the tetragonal and orthorhombic phases of barium titanate in the films.This work has been supported by Fundacao para a Ciencia e Tecnologia (FCT) and FEDER, through the projects PTDC/CTM/099415/2008 and PTDC/CTM-NAN/115125/2009 and by QREN-ON2-O Novo Norte, through the project Operacao Norte-070124-FEDER-000070. J. G. Barbosa and I. T. Gomes gratefully acknowledge PhD grants from Fundacao para a Ciencia e Tecnologia (SFRH/BD/41913/2007 and SFRH/BD/36348/2007, respectively)