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:
Which field theories belong in percolation universality classes?
What is percolation CFT?
What is field theory, that have "mean field" values for percolation universality class in $d≥6$?
