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Infra-red divergences in the large-N expansion

Bortolo Matteo Mognetti
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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 ϕ^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.

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Bortolo Matteo Mognetti. 2007-03-20. Infra-red divergences in the large-N expansion. https://arxiv.org/abs/hep-lat/0703020

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