On the range of validity of the 6-ε expansion for percolation

Abstract

In 6- epsilon dimensions the critical properties of percolation can be computed starting from a phi ³ theory having the same symmetry of the one-state Potts model. The authors argue that this fixed point must be unstable with respect to a phi ⁴ interaction in two dimensions; therefore a phi ⁴ perturbation is relevant. This suggestion is confirmed by an explicit two-loops computation.