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

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 $p_{\mathrm{\ne }}$. 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.