Logarithmic Corrections in Directed Percolation

TL;DR

This paper investigates the critical behavior of directed percolation at the upper critical dimension, focusing on logarithmic corrections to mean-field predictions for various cluster properties using renormalized dynamical field theory.

Contribution

It provides the first detailed calculation of leading and next-to-leading logarithmic corrections for directed percolation at the critical dimension d=4.

Findings

Derived explicit forms of logarithmic corrections for cluster mass, radius of gyration, and survival probability.

Calculated logarithmic corrections to the stationary particle density equation of state.

Confirmed the significance of logarithmic terms at the upper critical dimension in directed percolation.

Abstract

We study directed percolation at the upper critical transverse dimension $d=4$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) behavior. Viewing directed percolation as a kinetic process, we address the following properties of directed percolation clusters: the mass (the number of active sites or particles), the radius of gyration and the survival probability. Using renormalized dynamical field theory, we determine the leading and the next to leading logarithmic corrections for these quantities. In addition, we calculate the logarithmic corrections to the equation of state that describes the stationary homogeneous particle density in the presence of a homogeneous particle source.