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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).
Digital Object Identifer:10.1103/PhysRevE.73.016114
Published with permission from the copyright holder. This is the institute's copy, as published in Physical Review E, January 2006, Volume 73, Issue 1, Pages 6.
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Physical Review E
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