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

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

2005-12-18

arxiv.org/abs/cond-mat/0512421v1

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

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.73.016114

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).

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