Colored Percolation Theory

Colored Percolation is a generalization to conventional percolation schemes where occupied sites are colored with distinctive colors. A bond between two sites is open if the incident vertices are occupied and are of the same color. . Our goal for this project was to investigate the phenomena in three-dimensional lattices. We started with finding unique diagram configurations for every order and their respective perimeters. For the first time, we applied analytic diagram expansion for a multicomponent scenario. We employed Dlog-Pade approximants to analyze the perturbative analytical serious and calculate the transition temperatures as well as critical site occupancy probabilities.