Intermittency Studies in Directed Bond Percolation

TL;DR

This paper investigates the self-similar fluctuations in directed bond percolation at criticality, revealing intermittency patterns and deriving a new relation connecting intermittency indices with critical exponents and fractal dimensions.

Contribution

It introduces a novel analysis of intermittency in directed percolation using factorial moments and establishes a new theoretical relation between intermittency indices and critical properties.

Findings

Existence of weak but definite intermittency patterns

Fractal dimensions consistent with scaling arguments

New relation linking intermittency indices to critical exponents

Abstract

The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the factorial moments for large $1+1$-dimensional lattices allow to handle statistical and boundary effects and show the existence of weak but definite intermittency patterns. The extracted fractal dimensions are in agreement with scaling arguments leading to a new relation linking the intermittency indices to the critical exponents and the fractal dimension of directed percolation clusters.