Transport properties of directed percolation clusters at the upper critical dimension

Abstract

We study the transport properties of directed percolation clusters at the upper critical dimension $d_c=4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field theory and renormalization group methods we calculate these logarithmic corrections up to and including the next to leading correction for a variety of observables, viz. the connectivity, i.e., the probability that two given points are connected, the average two-point resistance and some of the fractal masses describing percolation clusters. Furthermore, we study logarithmic corrections for the multifractal moments of the current distribution on directed percolation clusters.

12 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday

References in corpus (5)

• The Field Theory Approach to Percolation Processes
• Universal scaling behavior of directed percolation around the upper critical dimension
• Logarithmic Corrections in Directed Percolation
• Logarithmic corrections to scaling in critical percolation and random resistor networks
• Logarithmic Corrections in Dynamic Isotropic Percolation