HK algorithm for comparing percolation threshold in square and triangular lattice using Python programing

  • Madhumita Nath et al.


Behaviors of flow phenomena through any regular or disordered medium can be described by percolation theory. The potential application of percolation theory ranges from medical science, cosmology, soil science, to complex material structure. In the present article, Monte Carlo simulation has been developed using high level programing language-Python to compare the site percolation threshold (pc) for the square and triangular lattice. For the development of the program, the inbuilt libraries of Python named NumPy, SciPy, Matplotlib etc were used. The cluster identification and numbering is based on Hoshen-Kopelman (HK) algorithm which consumes low computer memory as well as less computation time. The pc value computed for square and triangular lattice are 0.59 and 0.50 respectively. The percolation is also characterized by finding the ratio of normalized mass of cluster to normalized size of spanning cluster (Nmp). Present work is generous effort to represent Python as an efficient tool for coding in percolation theory. The realizations of percolation characteristics comparison by means of HK algorithm in square and triangular lattice using Python language is reported for the first time.