  We argue that the sharp-cutoff Wilson renormalization group provides a
powerful tool for the analysis of second-order and weakly first-order phase
transitions. In particular, in a computation no harder than the calculation of
the 1-loop effective potential, we show that the Wilson RG yields the fixed
point couplings and critical exponents of 3-dimensional $O(N)$ scalar field
theory, with results close to those obtained in high-order $\ep$-% expansion
and large-$N$ calculations. We discuss the prospects for an even more precise
computation.
