Connectivity-dependent properties of diluted sytems in a transfer-matrix description

Details Connectivity-dependent properties of diluted sytems in a transfer-matrix description Connectivity-dependent properties of diluted sytems in a transfer-matrix description

1998-04-27

arxiv.org/abs/cond-mat/9804286v1

Physical Review E 57, 6245R (1998)

Physics

Condensed Matter

Statistical Mechanics

4 pages, no figures, RevTeX, Phys. Rev. E Rapid Communications (to be published)

Scientific paper

10.1103/PhysRevE.57.R6245

We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in non-zero matrix elements and allows one to use standard random-matrix multiplication techniques. Thus it is possible to investigate physical processes on the percolation structure with the high efficiency and precision characteristic of transfer-matrix methods, while avoiding disconnections. The method is illustrated for two-dimensional site percolation by calculating (i) the critical correlation length along the strip, and the finite-size longitudinal DC conductivity: (ii) at the percolation threshold, and (iii) very near the pure-system limit.

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