The percolation threshold is a quantity which varies greatly from lattice to
lattice. However, the critical exponents do not depend on the details of
lattice geometry. They are the same for all lattices of the same dimensionality
D, i.e. the critical exponents are dimensional invariants.
For D = 2 the critical exponents are b =
0.14, g = 2.4, n =
1.35. Some important relations between these critical exponents follow
from scaling laws, e.g.
Dn = 2b + g.
It is amazing that the critical exponents do not depend on the nearest neighbor number. You see below "square" lattices with 4 neighbors (or 8 with diagonal sites), 6 and 3 neighbors.
4 6 | | | / | / \ / \ / - o - o - - o - o - - o - o - | | / | / | / ~ \ / \ / - o - o - - o - o - - o - o - | | / | / | / \ / \ 3 | / | \ / \ . o - o . o - o - o o - / | / / \ / - o . o - o . ~ - o o - o | / | \ / \ o - o . o - o o - o o -