Logarithmic corrections in dynamic isotropic percolation.

Abstract

Based on the field theoretic formulation of the general epidemic process, we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine these corrections for some of the most interesting time dependent observables in dynamic percolation at the critical point up to and including the next to leading correction. For clusters emanating from a local seed at the origin, we calculate the number of active sites, the radius of gyration, as well as the survival probability.