Percolation universality class

There’s very good table of different universality classes:

Ising model lies in the same universality class with $phi^4$ theory.
Ising in $d≥4$ have critical exponents for free scalar field.

But I don’t know field theories, which belong the percolation universality class. So I have few questions:

1. Which field theories belong in percolation universality classes?

2. What is percolation CFT?

3. What is field theory, that have "mean field" values for percolation universality class in $d≥6$?