Relation between a heterogeneous percolation model for cylinders and phase separation in the lattice fluid problem

A relationship based upon analogy is explored between (i) a lattice-based model for percolation by cylinders that employs distinct site types with unequal occupation probabilities in order to capture heterogeneities in the particle dispersion, and (ii) the well-studied mean-field lattice gas model. The strength of the correlation that sites in the percolation model that have distinct occupation probabilities are adjacent to each other maps into the coupling constant for the associated lattice fluid problem. Pursuing the analogy further, the vapor-liquid coexistence curve for the lattice gas translates into a phase boundary for the percolation problem, in terms of a locus of correlation strengths that demarcate a region of phase separation into sites with different occupation probabilities and distinct percolation thresholds. The dependence of the percolation thresholds in the one- and two-phase regions as delineated by this analogy are calculated as functions of the degree of disparity between site occupation probabilities and the strength of the correlation between adjacent site types.