A Monte-Carlo Analysis of Percolation of Line-Segments on a Square Lattice

TL;DR

This paper investigates how the percolation threshold of line-segments on a square lattice varies with segment length, revealing a non-monotonic behavior and structural changes in clusters, challenging universality class assumptions.

Contribution

It introduces a detailed analysis of percolation in systems with line-segments, highlighting non-monotonic thresholds and structural cluster changes, which differ from classical percolation models.

Findings

Percolation threshold decreases then increases with segment length

Structural changes in clusters explain non-monotonic behavior

Systems likely do not belong to the universality class of random site percolation

Abstract

We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and then increases slowly for large segments. We explain this non-monotonic behaviour by a structural change of the percolation clusters. Moreover, it is strongly suggested that these systems do not belong to the universality class of random site percolation.