Failure of length scaling in Wilson's ? expansion

We show that length scaling of the four-point scattering amplitude in Wilson's ? expansion is not consistent in the order of ?³. However, in conformity with conformal invariance at the critical point, momentum scaling in a given channel is consistent. This latter method permits us to calculate the dimension of the field φ² at the critical point without recourse to length scaling and one finds $\text{d}{}_{\mathrm{\phi }}\text{2 =}\text{d}\text{2}\text{?}\text{1}\text{ν}\text{to O}\text{(?}{}^2\text{)}$ as if length scaling were true. However, this does not imply Kadanoff's relation 2?α = νd which is predicted on length scaling. Indeed the above-mentioned inconsistency makes impossible the determination of α by these methods.