Statistics of Red Sites on Elastic and Full Backbone

TL;DR

This paper studies the scaling behavior of red sites on elastic and full backbones at the percolation threshold, revealing similarities and dimensionality-dependent exponents.

Contribution

It provides a comparative analysis of red site statistics on elastic and full backbones, highlighting how their exponents converge with increasing dimensionality.

Findings

Red sites scale similarly for elastic and full backbones at the percolation threshold.

The number of common red sites scales similarly for both backbones.

The elastic backbone exponent approaches the full backbone exponent as dimensionality increases.

Abstract

We investigate the number of red sites on the elastic and real backbone when right at the percolation threshold a spanning cluster exists between two sites at opposite faces of the lattice and found that it scales in the same way as in the case of percolation between two plates. We also find out that the number of common red sites scales similarly for both kinds of backbones for percolation between pairs of sites on opposite faces of the lattice. Our statistics for several quantities show that the the exponent for the elastic backbone approaches the one of the full backbone as dimensionality is increased.