Quenched disorder is very important but notoriously hard. In 1979, Parisi and Sourlas proposed an interesting and powerful conjecture about the infrared fixed points with random field (RF) type of disorder: such fixed points should possess an unusual supersymmetry, by which they reduce in two less spatial dimensions to usual non-supersymmetric non-disordered fixed points. The conjecture is known to hold for the RF φ^3 model but not for RF φ^4 model in d

IPhT