Bond percolation on square lattice — giant component & scaling near p_c
Bond probability p0.500
Grid size L30
Bond percolation: each edge activated with probability p. At p_c = 0.5 (square lattice), a giant connected component spanning the system emerges.
Near p_c: giant component size S ~ |p−p_c|^β with β = 5/36, correlation length ξ ~ |p−p_c|^{−ν} with ν = 4/3. Order parameter: fraction of sites in largest cluster P∞ → 0 below p_c, grows as (p−p_c)^β above. Colors show distinct clusters; red = largest.