Logarithmic Corrections in Dynamic Isotropic Percolation

TL;DR

This paper investigates logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension using renormalization group methods, focusing on time-dependent observables like active sites, survival probability, and radius of gyration.

Contribution

It provides the first detailed calculation of logarithmic corrections for key dynamic observables in isotropic percolation at the critical dimension.

Findings

Calculated logarithmic corrections for active sites, survival probability, and radius of gyration.

Extended understanding of critical behavior at the upper critical dimension.

Enhanced theoretical framework for dynamic percolation models.

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 survival probability as well as the radius of gyration.