  We investigate a $Z_2$-symmetric scalar field theory in two dimensions using
the Polchinski exact renormalization group equation expanded to second order in
the derivative expansion. We find preliminary evidence that the Polchinski
equation is able to describe the non-perturbative infinite set of fixed points
in the theory space, corresponding to the minimal unitary series of 2D
conformal field theories. We compute the anomalous scaling dimension $\eta$ and
the correlation length critical exponent $\nu$ showing that an accurate fit to
conformal field theory selects particular regulating functions.
