Infra-red divergences in the large-N expansion

TL;DR

This paper studies infra-red divergences in large-N models near critical points, revealing a universal crossover mechanism between mean-field and nonclassical universality classes, across various models including vector, Yukawa, and 6 models.

Contribution

It introduces a generalized 1/N expansion framework that explains infra-red divergences as a universal crossover phenomenon in large-N models.

Findings

Infra-red divergences are linked to a universal crossover mechanism.

The crossover occurs between mean-field and nonclassical universality classes.

Multicritical points are also analyzed within this framework.

Abstract

We investigate a vectorial O(N) model with a generic nearest-neighbor interaction W(\bsigma_i\cdot \bsigma_j) (depending on {\cal N} tunable parameters), a Yukawa (and Gross Neveu) model with N_f fermions at finite temperature and the vectorial \phi^6 model, in the large N (N_f) limit. All this models exhibit a Mean Field critical point for N=\infinity. When 1/N fluctuations are included, infra red divergences appear near the critical point. In the framework of a generalized 1/N expansion we show that these divergences are related to a universal crossover mechanism between the Mean Field universality class (N=\infinity) and the nonclassical one for N<\infinity. For the generic nearest-neighbor interaction multicritical points are also investigated.