Critical exponents from two-particle irreducible 1/N expansion

TL;DR

This paper computes the critical exponent nu for the O(N) phi^4 model using a two-particle-irreducible (2PI) 1/N expansion, providing improved results over traditional methods by deriving and solving a self-consistent equation for the vertex function.

Contribution

It introduces a novel 2PI 1/N expansion approach to calculate the critical exponent nu, enhancing accuracy over standard 1PI calculations.

Findings

Next-to-leading order results improve previous estimates.

Derived a self-consistent equation for the vertex function.

Applied the method to the O(N) symmetric phi^4 model in 3D.

Abstract

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.