Is there a link between Percolation Theory and phase transitions?

Is there a direct link between phase transitions in physics and Percolation Theory (and the critical points in both cases) in the sense that the mechanism in one of them could be a special or generalized case of the other?

• Percolation is a phenomenon characterised by the fact that a "typical" length blowsup. Note that the length can be thought as a correlation between local observables, but this is not necessary. Under a rescaling of the system - in this case the rescaling is given by zooming out but in other case it could be zooming in or integrating away small or fast energies - this length has to scale. However if it is infinity, the rescaling leave it unaffected, hence the system looks the same at every ditance. This happens anytime you have a 2nd order phase transition. – giulio bullsaver Oct 18 '17 at 14:33