Transfer-matrix approach to three-dimensional bond percolation: an application of Novotny's formalism.
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).
Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan.
Yoshihiro
Y
Nishiyama