Critical Exponents without the Epsilon Expansion

Abstract

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.