English

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

Statistical Mechanics 2009-10-31 v1 Disordered Systems and Neural Networks

Abstract

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.

Keywords

Cite

@article{arxiv.cond-mat/9804286,
  title  = {Connectivity-dependent properties of diluted sytems in a transfer-matrix description},
  author = {S. L. A. de Queiroz and R. B. Stinchcombe},
  journal= {arXiv preprint arXiv:cond-mat/9804286},
  year   = {2009}
}

Comments

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