Critical exponents from the two-particle irreducible 1/N expansion

We calculate the critical exponent nu of the O(N) symmetric phi(4) model within the 1/N expansion of the two-particle-irreducible effective action, which provides us with a self-consistent approximation scheme for the correlation function. The exponent nu controls the behavior of a two-point function <phi phi > near the critical point T not equal T-c through the correlation length xi similar to vertical bar T - Tc vertical bar(-nu), but we notice that it appears also in the scaling form of the three-point vertex function Gamma (2,1) similar to <phi phi phi(2)> at the critical point T Tc; in the momentum space, Gamma((2,1)) -kappa(2-eta-1/nu). We derive a self-consistent equation for Gamma((2,1)) from the two-particle-irreducible effective action including the skeleton diagrams up to the next-leading-order in the 1/N expansion, and solve it to the leading-log accuracy (i.e., keeping the leading lnk terms) to obtain nu. Our results turn out to improve those obtained in the standard one-particle-irreducible calculation at the next-leading-order.