Stable fixed points in models with many coupling constants

Renormalisation group studies in d=4- epsilon dimensions have thus far indicated that landau-Ginzburg-Wilson (LGW) models with large numbers of fourth-order invariants do not possess a stable fixed point for small epsilon . This suggests that the existence of a stable fixed point is simply related to the number of fourth-order invariants. The authors show that no such simple relationship exists by constructing LGW models with both arbitrarily large numbers of invariants and a stable fixed point.