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We study the critical behavior of various geometrical and transportproperties of percolation in 6 dimensions. By employing field theory andrenormalization group methods we analyze fluctuation induced logarithmiccorrections to scaling up to and including the next to leading correction. Ourstudy comprehends the percolation correlation function, i.e., the probabilitythat 2 given points are connected, and some of the fractal masses describingpercolation clusters. To be specific, we calculate the mass of the backbone,the red bonds and the shortest path. Moreover, we study key transportproperties of percolation as represented by the random resistor network. Weinvestigate the average 2-point resistance as well as the entire family ofmultifractal moments of the current distribution.Comment: 14 pages, 1 figure, version to appear in Phys. Rev.

Logarithmic corrections to scaling in critical percolation and random resistor networks