Percolation is a logarithmic CFT. Among other things, this means it is not unitary.

This page focuses on “standard percolation” — see Related theories below for alternative definitions that yield different CFTs.

Percolation is

Because percolation is not a unitary CFT, there is no Hamiltonian lattice theory that flows to percolation in the IR.

Percolation in one dimension is, unsurprisingly, exactly solvable. Clearly no critical cluster can exist unless $p=1$, so that's the critical point. Working out the average cluster size at arbitrary $p$ can be an exercise.

In six or more dimensions critical percolation is described by mean-field theory.

• Directed percolation