Application of the central-particle-potential approximation for percolation in interacting systems

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Abstract
We compute the percolation threshold of systems of interacting particles by a random-adding algorithm with a rejection criterion based on the density distribution of the particles. The results are very close to those obtained in our previous work based on a simple Boltzmann central-particle approximation. The results are also essentially the same as those obtained by the Metropolis method, even though our algorithm is conceptually different and does not generate a true equilibrium configuration. This finding suggests that connectivity, in comparison with other system properties, is more ‘‘general’’ and is not sensitive to the particulars of the equilibrium state. Thus, our findings offer an efficient method for obtaining percolation thresholds in systems of interacting particles. This method is computationally simpler and faster than the well known Metropolis method.