  We study the critical behavior of various geometrical and transport
properties of percolation in 6 dimensions. By employing field theory and
renormalization group methods we analyze fluctuation induced logarithmic
corrections to scaling up to and including the next to leading correction. Our
study comprehends the percolation correlation function, i.e., the probability
that 2 given points are connected, and some of the fractal masses describing
percolation clusters. To be specific, we calculate the mass of the backbone,
the red bonds and the shortest path. Moreover, we study key transport
properties of percolation as represented by the random resistor network. We
investigate the average 2-point resistance as well as the entire family of
multifractal moments of the current distribution.
