Estimates of threshold and strength of percolation clusters on square lattices with (1,)-neighborhood

Abstract

In this paper we consider statistical estimates of threshold and strength of percolation clusters on square lattices. The percolation threshold pc and the strength of percolation clusters P for a square lattice with (1,)-neighborhood depends not only on the lattice dimension, but also on the Minkowski exponent d. To estimate the strength of percolation clusters P proposed a new method of averaging the relative frequencies of the target subset of lattice sites. The implementation of this method is based on the SPSL package, released under GNU GPL-3 using the free programming language R.

Keywords

• site percolation
• square lattice
• non-metric Minkowski distance
• Moore neighborhood
• percolation threshold
• strength of infinite clusters
• R programming language
• SPSL package