Large N planar approximation and critical behavior of a SU(N) invariant four fermion model in (2+1)-dimensions
Sep, 2001Citations per year
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
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