Critical exponents from two-particle irreducible 1/N expansion

We calculate the critical exponent $\nu$ in the 1/N expansion of the two-particle-irreducible (2PI) effective action for the O(N) symmetric $\phi ^4$modelinthreespatialdimensions\mathrm{.}Theexponent$\nu$ controls the behavior of a two-point function $<\varphi \varphi >$ {\it near} the critical point $T\neq T_c$,butcanbeevaluatedonthecriticalpoint$T=T_c$ by the use of the vertex function ${\mathrm{\Gamma }}^{(2,1)}$. We derive a self-consistent equation for ${\mathrm{\Gamma }}^{(2,1)}$ within the 2PI effective action, and solve it by iteration in the 1/N expansion. At the next-to-leading order in the 1/N expansion, our result turns out to improve those obtained in the standard one-particle-irreducible calculation.