High-order behavior in φ3 field theories and the percolation problem

The percolation problem is normally described in field theory by the n-->0 limit of the n-component Potts model. This model has trilinear interactions which give rise to an ɛ expansion in 6-ɛ dimensions. In contrast to positive values of n, the n=0 case is shown to have oscillatory growth at high orders in ɛ which permits Padé-Borel resummation. A new formulation of the n=0 limit is required to obtain this result. An improved estimate is given for the critical exponent ω which describes corrections to scaling.