Polchinski equation, reparameterization invariance and the derivative expansion

The connection between the anomalous dimension and some invariance properties of the fixed point actions within exact RG is explored. As an application, the Polchinski equation at next-to-leading order in the derivative expansion is studied. For the Wilson fixed point of the one-component scalar theory in three dimensions we obtain the critical exponents η = 0.042, ν = 0.622 and ω = 0.754.