THE DERIVATIVE EXPANSION OF THE RENORMALIZATION-GROUP

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).