Abstract: In a regular lattice, the active sites infect their neighboring vacant sites with a certain probability step by step. A grand canonical ensemble was finally formed by all the occupied sites. To represent the system by the partition function of the ensemble, we have substituted the infect probability for the system temperature and divided the energy levels of the sites with different steps. The percolation phase transition of this system at percolation threshold Pc was substantiated by Monte Carlo simulation. Thus a new general method is established, in which the intrinsic behavior of the lattice in the dynamic process of particle growth and other infection growth is used, to estimate the percolation threshold of any lattice. The validity of the model was experimentally verified by studying the growth process of the nanometal films on a dielectric substrate. A proper explanation of the connection between the model and the physical substance was also given.

Keywords: 
• percolation /
• ensemble /
• Monte Carlo /
• growth model