Critical exponents from two-particle irreducible 1/N expansion

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

2011-08-05

arxiv.org/abs/1108.1266v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

18 pages

Scientific paper

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.

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