  We calculate the critical exponent $\nu$ in the 1/N expansion of the
two-particle-irreducible (2PI) effective action for the O(N) symmetric $\phi
^4$ model in three spatial dimensions. The exponent $\nu$ controls the behavior
of a two-point function $<\phi \phi>$ {\it near} the critical point $T\neq
T_c$, but can be evaluated on the critical point $T=T_c$ by the use of the
vertex function $\Gamma^{(2,1)}$. We derive a self-consistent equation for
$\Gamma^{(2,1)}$ 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.

High Energy Physics - Phenomenology