Nonmonotonical behavior in correlated site-bond percolation

Site-bond percolation is addressed in a very general class of correlated site-bond systems. The site-bond model analyzed provides a simple natural picture of disordered media such as porous materials, nonuniform surfaces adsorption potential, conductivity of inhomogeneous systems, and landscapes. The bond (site) percolation threshold exhibits a nonmonotonical behavior, showing maxima and minima as statistical correlation of two-point lattice properties varies from zero to one. Phase diagrams for the general case of correlated site-bond percolation are obtained by Monte Carlo simulation. The continuum percolation limit is recovered for percolation at maximum correlation.