Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism

TL;DR

This paper introduces a transfer-matrix simulation scheme for three-dimensional bond percolation using Novotny's formalism, allowing systematic finite-size scaling analysis and estimation of the critical exponent.

Contribution

It applies Novotny's transfer-matrix formalism to 3D bond percolation, enabling analysis with arbitrary system sizes for improved criticality estimation.

Findings

Estimated critical exponent nu = 0.81(5)

Systematic finite-size scaling analysis performed

Transfer matrix diagonalization for N=4 to 10

Abstract

A transfer-matrix simulation scheme for the three-dimensional (d=3) bond percolation is presented. Our scheme is based on Novotny's transfer-matrix formalism, which enables us to consider arbitrary (integral) number of sites N constituting a unit of the transfer-matrix slice even for d=3. Such an arbitrariness allows us to perform systematic finite-size-scaling analysis of the criticality at the percolation threshold. Diagonalizing the transfer matrix for N =4,5,...,10, we obtain an estimate for the correlation-length critical exponent nu = 0.81(5).