Scheme independence and the exact renormalization group

We compute critical exponents in a Z2 symmetric scalar field theory in three dimensions, using Wilsonʹs exact renormalization group equations expanded in powers of derivatives. A nontrivial relation between these exponents is confirmed explicitly at the first two orders in the derivative expansion. At leading order all our results are cutoff independent, while at next-to-leading order they are not, and the determination of critical exponents becomes ambiguous. We discuss the possible ways in which this scheme ambiguity might be resolved.