Logarithmic corrections to scaling in critical percolation and random resistor networks

Abstract

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.

14 pages, 1 figure, version to appear in Phys. Rev. E

References in corpus (1)

• Critical Percolation in High Dimensions

Cited by in corpus (8)

• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• From discrete to continuous percolation in dimensions 3 to 7
• Normal form for renormalization groups
• Universal scaling behavior of directed percolation around the upper critical dimension
• Logarithmic Corrections in Directed Percolation
• Multifractality in a broad class of disordered systems
• Transport properties of directed percolation clusters at the upper critical dimension