Four-fermi interaction in (2+1) dimensions beyond leading order in 1/N

Gat, G.; Kovner, Alex; Rosenstein, Baruch; Warr, Brian J.

doi:10.1016/0370-2693(90)90425-6

Cited by 47 publications

(37 citation statements)

References 12 publications

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“…After performing the renormalization procedure [3,8,9], we can obtain the physical mass spectra ' -z r p ) . (o,o;o)( $$) mf -* *,*,G where we have used Z+= 1 to leading order [13]. This is in agreement with the result in the large-N expansion [4].…”

Section: R[+]= W [ J ] I Ddx (Rj(x)$c(x)+~(x)rl~x)+[~c(x)$c~x)+~(x)lsupporting

confidence: 83%

Chiral Ward-Takahashi identities and mass spectra in (2+1)-dimensional chiral Gross-Neveu model

Kun

Zhongping

1992

Phys. Rev. D

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Based on chiral Ward-Takahashi identities with composite fields, we develop a method to investigate fermion mass generation and bound-state spectra in the ( 2 + 1 )-dimensional chiral Gross-Neveu model. PACS number(s): 11.15.Ex, 11.30.RdAlthough it is commonly accepted that QCD is the theory of strong interactions, at nuclear length scales the coupling constant is really strong and does not allow for a systematic perturbative expansion, which means that nonperturbative schemes ought to be taken into account. Because of the inherent difficulties in attempting to study nonperturbative phenomena [I], the bound-state spectra and chiral symmetry in QCD are still unsolved problems [2]. Since chiral symmetry and nonperturbative phenomena can be easily analyzed in certain models, chiral symmetry and the bound-state spectra in QCD are investigat-features which are expected from QCD, i.e., asymptotic freedom, dynamical symmetry breaking, and dynamical mass generation [4]; it is expected that the properties of the chiral Gross-Neveu model will help us understand the low-energy properties in QCD. Considering the spontaneous breaking of a continuous symmetry does not occur in two space-time dimensions [S], we take the (2 + 1 )-dimensional chiral Gross-Neveu model as an example.The Lagrangian density is given by ed in some models.

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Section: R[+]= W [ J ] I Ddx (Rj(x)$c(x)+~(x)rl~x)+[~c(x)$c~x)+~(x)lsupporting

confidence: 83%

Chiral Ward-Takahashi identities and mass spectra in (2+1)-dimensional chiral Gross-Neveu model

Kun

Zhongping

1992

Phys. Rev. D

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“…The natural counterparts of the bosonic models we have discussed are theories with four-Fermi interactions and U(N) symmetry, powercounting renormalizable in two dimensions and 1/N expandable. These theories are ultraviolet renormalizable order by order in the 1/N expansion in less than four dimensions, as shown by Rosenstein and coworkers [179][180][181] and by Kikukawa and Yamawaki [182], essentially because their ultraviolet limit has the same relevant operator content as the infrared limit of the superrenormalizable Yukawa model. These arguments were further developed in Refs.…”

Section: Fermionic Modelsmentioning

confidence: 84%

The 1/N expansion of two-dimensional spin models

Campostrini

Rossi

1993

Riv. Nuovo Cim.

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A short review of all available results (perturbative, nonperturbative, and exact) on d-dimensional spin models is presented in order to introduce the discussion of their 1/N expansion at d = 2, where the models are asymptotically free.A general two-dimensional spin model with U(N ) invariance, interpolating between CP N −1 and O(2N ) models, is studied in detail in order to illustrate both the general features of the 1/N expansion on the lattice and the specific techniques devised to extract scaling (field-theoretical) behavior. The continuum version of the model is carefully analyzed deriving quantitative O(1/N ) physical predictions in order to establish a benchmark for lattice computations.The 1/N expansion on the lattice, including second-nearest-neighbor interactions, is set up by constructing explicitly effective propagators and vertices, and exhibiting a number of exact results and integral representations that allow a substantial reduction of the numerical effort. The technique of asymptotic expansion of the lattice propagators, basic to the derivation of analytical results in the scaling domain, is presented in full detail and applied to the model. Physical quantities, like the free energy and different definitions of correlation length, are evaluated.The lattice renormalization-group trajectories are identified and universality among different lattice (and continuum) schemes in the scaling region is explicitly proven. As a byproduct, representations of the O(1/N ) contribution to the Λ-parameter ratios and to the lattice β functions are obtained.A review of other developments based on the lattice 1/N expansion (finite size scaling, higher orders, fermionic models) is presented.

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“…We believe that the next-toleading-order computation both demonstrates the renormalizability of the-four-~ermi theory and provides an aid in estimating the radius of convergence of the large-N expansion. There is a previous result on the renormaliza-tion in large-N with a single four-Fermi coupling and without further coupling to electromagnetic interactions [28]. There it is asserted that an additive renormalization of the auxiliary scalar fields of the model is necessary.…”

Section: Introductionmentioning

confidence: 97%

Dynamical violation of parity and chiral symmetry in three-dimensional four-Fermi theory

Semenoff

Wijewardhana

1992

Phys. Rev. D

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We study dynamical symmetry breaking in (2+ lbdimensional quantum electrodynamics with four-Fermi couplings. Using the large-N expansion and an effective potential method we show that the four-Fermi couplings can be relevant when the coupling constants are near certain critical points. We show that the four-Fermi interactions can break either parity and time-reversal symmetries or a certain discrete flavor symmetry and analyze how the symmetry-breaking pattern is modified by electromagnetic interactions. We discuss the critical behavior of the theory in the large-N expansion in both the leading and next-to-leading orders.

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Four-fermi interaction in (2+1) dimensions beyond leading order in 1/N

Cited by 47 publications

References 12 publications

Chiral Ward-Takahashi identities and mass spectra in (2+1)-dimensional chiral Gross-Neveu model

Chiral Ward-Takahashi identities and mass spectra in (2+1)-dimensional chiral Gross-Neveu model

The 1/N expansion of two-dimensional spin models

Dynamical violation of parity and chiral symmetry in three-dimensional four-Fermi theory

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