Critical exponents from two-particle irreducible 1/N expansion

We calculate the critical exponent $ν$ in the 1/N expansion of the two-particle-irreducible (2PI) effective action for the O(N) symmetric $ϕ^4$ model in three spatial dimensions. The exponent $ν$ controls the behavior of a two-point function $<ϕϕ>$ {\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 $Γ^{(2,1)}$. We derive a self-consistent equation for $Γ^{(2,1)}$ 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.

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