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Large N planar or bare vertex approximation and critical behavior of a SU(N) invariant four-fermion model in 2+1 dimensions

Manuel Reenders
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Abstract

A four-fermion model in 2+1 dimensions describing N Dirac fermions interacting via SU(N) invariant N^2-1 four-fermion interactions is solved in the leading order of the 1/N expansion. The 1/N expansion corresponds to 't Hoofts topological 1/N expansion in which planar Feynman diagrams prevail. For the symmetric phase of this model, it is argued that the planar expansion corresponds to the ladder approximation. A truncated set of Schwinger-Dyson equations for the fermion propagator and composite boson propagator representing the relevant planar diagrams is solved analytically. The critical four-fermion coupling and various critical exponents are determined as functions of N. The universality class of this model turns out to be quite distinct from the Gross-Neveu model in the large N limit.

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Manuel Reenders. 2002-09-30. Large N planar or bare vertex approximation and critical behavior of a SU(N) invariant four-fermion model in 2+1 dimensions. https://arxiv.org/abs/hep-th/0109016

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