Derivative expansion of the renormalization group in O(N) scalar field theory

We apply a derivative expansion to the Legendre effective action flow equations of O(N) symmetric scalar field theory, making no other approximation. We calculate the critical exponents η, ν, and ω at the both the leading and second order of the expansion, associated to the three dimensional Wilson-Fisher fixed points, at various values of N . In addition, we show how the derivative expansion reproduces exactly known results, at special values N = ∞,−2,−4, · · ·.