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Percolation problem

General info

The site percolation problem on a square lattice and each site of a lattice is occupied independently with probability p. In Monte Carlo simulation, we investigate

  • connection between the first and the last row: The Burning Method
  • distribution of clusters: Hoshen–Kopelman algorithm

Code implementation has made in Python3. Trials configurations of system was made by use pseudo-random numbers and advantage of Python is that core of library generate random numbers use the Mersenne Twister generator which is really good for simulations.

Results

  1. plot_percolation_threshold.png -> probability that there is connection between two sides of lattice
  2. plot_min_path.png -> the shortest path between two sides of lattice
  3. plot_average_cluster.png -> average size of clusters
  4. plot_maximum_cluster.png -> maximum size of clusters

Run

Because of different complexity of used algorithms, we run both methods separately (initial parameters: config.json)

python3 main.py --method burning

python3 main.py --method clustering