Alternative criterion for two-dimensional wrapping percolation

TL;DR

This paper introduces an alternative criterion for testing wrapping percolation in two-dimensional lattices, using finite size scaling and the Newman-Ziff method, with results aligning with existing methods.

Contribution

It proposes a new criterion for wrapping percolation testing in 2D lattices, enhancing the understanding of percolation thresholds.

Findings

The new criterion is consistent with Machta's method.

Finite size scaling estimates for percolation thresholds are provided.

Results validate the effectiveness of the alternative criterion.

Abstract

Based on the differences between a spanning cluster and a wrapping cluster, an alternative criterion for testing wrapping percolation is provided for two-dimensional lattices. By following the Newman-Ziff method, the finite size scaling of estimates for percolation thresholds are given. The results are consistent with those from Machta's method.