Test of multiscaling in DLA model using an off-lattice killing-free algorithm

TL;DR

This study introduces a modified off-lattice algorithm for DLA that avoids particle killing, enabling more accurate analysis of multiscaling and fractal dimensions in large clusters, revealing weak self-averaging and nonmonotonic behavior.

Contribution

The paper presents a novel off-lattice, killing-free algorithm for DLA that allows large-scale simulations and detailed multiscaling analysis, addressing previous methodological limitations.

Findings

Multiscaling cannot be conclusively ruled out.

Fractal dimension is a weak self-averaging quantity.

Fractal dimension calculated via harmonic measure is nonmonotonic with cluster size.

Abstract

We test the multiscaling issue of DLA clusters using a modified algorithm. This algorithm eliminates killing the particles at the death circle. Instead, we return them to the birth circle at a random relative angle taken from the evaluated distribution. In addition, we use a two-level hierarchical memory model that allows using large steps in conjunction with an off-lattice realization of the model. Our algorithm still seems to stay in the framework of the original DLA model. We present an accurate estimate of the fractal dimensions based on the data for a hundred clusters with 50 million particles each. We find that multiscaling cannot be ruled out. We also find that the fractal dimension is a weak self-averaging quantity. In addition, the fractal dimension, if calculated using the harmonic measure, is a nonmonotonic function of the cluster radius. We argue that the controversies in the data interpretation can be due to the weak self-averaging and the influence of intrinsic noise.