Connectivity-dependent properties of diluted sytems in a transfer-matrix description

TL;DR

This paper presents a transfer-matrix based method to analyze connectivity-dependent properties of diluted systems, enabling efficient and precise investigation of percolation phenomena without disconnections.

Contribution

A novel transfer-matrix approach that incorporates connectivity properties for studying diluted systems, improving analysis of percolation characteristics.

Findings

Calculated critical correlation length along the strip.

Determined finite-size longitudinal DC conductivity.

Analyzed properties at the percolation threshold and near the pure system.

Abstract

We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in non-zero matrix elements and allows one to use standard random-matrix multiplication techniques. Thus it is possible to investigate physical processes on the percolation structure with the high efficiency and precision characteristic of transfer-matrix methods, while avoiding disconnections. The method is illustrated for two-dimensional site percolation by calculating (i) the critical correlation length along the strip, and the finite-size longitudinal DC conductivity: (ii) at the percolation threshold, and (iii) very near the pure-system limit.