Abstract: In this article we use the Schwinger-Dyson equations to compute the nonperturbative modifications caused to the infrared finite gluon propagator (in the Landau gauge) by the inclusion of a small number of quark families. Our basic operating assumption is that the main bulk of the effect stems from the "one-loop dressed'' quark loop contributing to the full gluon self-energy. This quark loop is then calculated, using as basic ingredients the full quark propagator and quark-gluon vertex; for the quark propagator we use the solution obtained from the quark-gap equation, while for the vertex we employ suitable Ansatze, which guarantee the transversality of the answer. The resulting effect is included as a correction to the quenched gluon propagator, obtained in recent lattice simulations. Our main finding is that the unquenched propagator displays a considerable suppression in the intermediate momentum region, which becomes more pronounced as we increase the number of active quark families. The influence of the quarks on the saturation point of the propagator cannot be reliably computed within the present scheme; the general tendency appears to be to decrease it, suggesting a corresponding increase in the effective gluon mass. The renormalization properties of our results, and the uncertainties induced by the unspecified transverse part of the quark-gluon vertex, are discussed. Finally, the gluon propagator is compared with the available unquenched lattice data, showing rather good agreement.

Abstract: Two metallacyclic complexes of general formula Na-8[(M2L3)-L-II]center dot xH(2)O [M = Ni (4) and Co (5) with x = 15 (4) and 17 (5)] have been self-assembled in aqueous solution from N,N'-1,3-phenylenebis(oxamic acid) (H4L) and M2+ ions in a ligand/metal molar ratio of 3 : 2 in the presence of NaOH acting as base. X-Ray structural analyses of 4 and 5 show triple-stranded, dinuclear anions of the meso-helicate-type (so-called mesocates) with C-3h molecular symmetry. The two octahedral metal-tris(oxamate) moieties of opposite chiralities (Delta, Lambda form) are connected by three m-phenylene spacers at intermetallic distances of 6.822(2) (4) and 6.868(2) angstrom (5) to give a metallacryptand core. In the crystal lattice, the binding of these heterochiral dinickel(II) and dicobalt(II) triple mesocates to sodium(I) ions leads to oxamato-bridged heterobimetallic three-dimensional open-frameworks with a hexagonal diamond architecture having small pores of 17.566(4) (4) and 17.640(2) angstrom (5) in diameter where the crystallization water molecules and the sodium(I) countercations are hosted. Variable temperature (2.0-300 K) magnetic susceptibility measurements reveal relatively anisotropic S = 2 Ni-2(II) (4) and S = 3 Co-2(II) (5) ground states resulting from the moderate to weak intramolecular ferromagnetic coupling between the two high-spin Ni-II (S-Ni = 1) or Co-II (S-Co = 3/2) ions across the m-phenylenediamidate bridges [J = +3.6 (4) and +1.1 cm(-1) (5); H = -JS(1)center dot S-2]. A simple molecular orbital analysis of the electron exchange interaction identifies the p-type pathways of the meta-substituted phenylene spacers involving the d(z2) and d(x2-y2) pairs of magnetic orbitals of the two trigonally distorted octahedral high-spin M-II ions (M = Ni and Co) as responsible for the overall ferromagnetic coupling observed in 4 and 5 in agreement with a spin polarization mechanism. The decrease of the overall ferromagnetic coupling from 4 to 5 is in turn explained by the additional antiferromagnetic exchange contribution involving the d(xy) pair of magnetic orbitals of the two trigonally distorted octahedral high-spin Co-II ions across the sigma-type pathway of the meta-substituted phenylene spacers.