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

2005/12/18 by Yoshihiro Nishiyama
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.73.016114

published as Phys. Rev. E 73, 016114 (2006).

arxiv created 2005/12/18 · openalex publication_date 2006/01/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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,..., we obtain an estimate for the correlation-length critical exponent v=0.81(5).

Citations

• Complex-temperature phase diagrams for theq-state Potts model on self-dual families of graphs and the nature of theq→∞limit
• Percolation on two- and three-dimensional lattices
• Scaling corrections: site-percolation and Ising model in three dimensions