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

Sep, 2001
14 pages
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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.
  • four-fermion interaction
  • symmetry: SU(N)
  • dimension: 3
  • expansion 1/N
  • approximation: planar
  • critical phenomena
  • perturbation theory: higher-order
  • mass spectrum
  • scaling
  • Dyson-Schwinger equation: solution