Phenomenological approach to finding the critical indices for 3D percolation in multifractal media

The percolation theory is applied widely to the study of heat transfer and other kinetic processes in systems with disordered structures. This paper develops a phenomenological approach that combines the percolation theory methods and multifractal analysis to model a percolation cluster in 3D infinite medium with multifractal properties. The developed model gives unambiguous numerical values for topology-critical indices and a critical conductivity index. The model reveals new relations between critical indices and defines the threshold conditions that separate the qualitatively-different modes of system behavior in the correlation length scales. The system order parameter has a relation with the golden ratio and this indicates a universal nature of the found relationships.