Phase Transitions in a Two-Component Site-Bond Percolation Model

Details Phase Transitions in a Two-Component Site-Bond Percolation Model Phase Transitions in a Two-Component Site-Bond Percolation Model

1999-07-21

arxiv.org/abs/cond-mat/9907330v1

Phys.Rev.B62:8719-8724,2000

Physics

Condensed Matter

Disordered Systems and Neural Networks

RevTeX, 5 pages, 5 eps-figures

Scientific paper

10.1103/PhysRevB.62.8719

A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices the percolation threshold in terms of $p_{+}$ is determined for N=2. Phase transitions are reported in two limits for the bond existence probabilities $p_{=}$ and $p_{\neq}$. In the same limits, empirical formulas for the percolation threshold $p_{+}^{c}$ as function of one component-concentration, $f_{b}$, are proposed. In the limit $p_{=} = 0$ a new site percolation threshold, $f_{b}^{c} \simeq 0.145$, is reported.

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