Finite-size scaling in asymmetric systems of percolating sticks

TL;DR

This paper studies how the finite size and aspect ratio of systems of percolating sticks affect their percolation behavior, introducing a generalized scaling function and identifying aspect ratio effects.

Contribution

It introduces a generalized scaling function for percolation in asymmetric stick systems and reveals aspect ratio dependencies and invariances in percolation probability.

Findings

Prefactors depend on aspect ratio.

Existence of a characteristic aspect ratio with scale-invariant percolation probability.

Parity properties of the scaling function's prefactors.

Abstract

We investigate finite size scaling in percolating widthless stick systems with variable aspect ratios in an extensive Monte Carlo simulation study. A generalized scaling function is introduced to describe the scaling behavior of the percolation distribution moments and probability at the percolation threshold. We show that the prefactors in the generalized scaling function depend on the system aspect ratio and exhibit features that are generic to whole class of the percolating systems. In particular, we demonstrate existence of characteristic aspect ratio for which percolation probability at the threshold is scale invariant and definite parity of the prefactors in generalized scaling function for the first two percolation probability moments.