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Site Percolation: Basic Definitions

Interactive Square Lattice

Occupation Probability (p): 0.50

Cluster Statistics:

Key Definitions

Parameters:

  • $L$: Lattice size (dimensionless)

    Number of sites along each dimension of the square lattice

  • $p$: Occupation probability

    Probability that any given site is occupied (dark)

  • $s$: Cluster size

    Number of occupied sites in a connected group

  • $N(s,p;L)$: Cluster frequency

    Number of clusters of size s at probability p on lattice size L

Nearest Neighbors:

In a square lattice, each bulk site has:

  • 4 nearest neighbors: North, South, East, West
  • 4 next-nearest neighbors: NE, NW, SE, SW (not used in basic site percolation)