By writing tile flow equations for the continuum Legendre effective ac
tion (a.k.a. Helmholtz free energy) with respect to a particular form
of smooth cutoff, and performing a derivative expansion up to some max
imum order, a set of differential equations are obtained which at FPs
(Fixed Points) reduce to non-linear eigenvalue equations for the anoma
lous scaling dimension eta. Illustrating this by expanding (single com
ponent) scalar field theory, in two, three and four dimensions, up to
second order in derivatives, we show that the method is a powerful and
robust means of discovering and quantifying non-perturbative continuu
m limits (continuous phase transitions).