Universality and Asymptotic Scaling in Drilling Percolation

TL;DR

This paper investigates a 3D percolation model with cylindrical holes, confirming previous findings with improved simulations and exploring potential asymptotic behaviors and generalizations.

Contribution

Introduces a more efficient simulation algorithm for the 3D drilling percolation model and examines its asymptotic properties and potential generalizations.

Findings

Results largely confirm previous studies despite larger system sizes.

Indications that the observed behavior may not yet be the true asymptotic limit.

Discussion of possible extensions of the model.

Abstract

We present simulations of a 3-d percolation model studied recently by K.J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016)], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present paper, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.