Random-adding determination of percolation thresholds in interacting systems

A generalization of the random-adding procedure for the determination of percolation parameters in interacting systems is demonstrated. This method which simply utilizes the Boltzmann distribution function is shown to reproduce quite accurately results which were obtained previously by the much less efficient and much less direct method of the Metropolis algorithm. The success of the present method is attributed to the fact that, for typical objects considered in such systems, the effect of the square-well attractive interaction compensates for the effect of the (hard-core) repulsive interaction on the spatial distribution of the objects around a given object.