Constructing the three-dimensional Gross-Neveu model with a large number of flavor components

Calan, C. de; Veiga, Paulo A. Faria da; Magnen, J. Le; Sénéor, Roland

doi:10.1103/physrevlett.66.3233

Cited by 84 publications

(76 citation statements)

References 13 publications

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“…That this is indeed the case in d = 3 has only recently been proven using the renormalization group technique of constructive field theory [17].…”

Section: Introductionmentioning

confidence: 99%

Four-Fermion Theory and the Conformal Bootstrap

Chen¹,

Makeenko²,

Semenoff³

1993

Annals of Physics

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We employ the conformal bootstrap to re-examine the problem of finding the critical behavior of four-Fermion theory at its strong coupling fixed point. Existence of a solution of the bootstrap equations indicates self-consistency of the assumption that, in space-time dimensions less than four, the renormalization group flow of the coupling constant of a four-Fermion interaction has a nontrivial fixed point which is generally out of the perturbative regime. We exploit the hypothesis of conformal invariance at this fixed point to reduce the set of the Schwinger-Dyson bootstrap equations for four-Fermion theory to three equations which determine the scale dimension of the Fermion field ψ, the scale dimension of the composite fieldψψ and the critical value of the Yukawa coupling constant. We solve the equations assuming this critical value to be small. We show that this solution recovers the fixed point for the four-fermion interaction with N -component fermions in the limit of large N at (Euclidean) dimensions d between two and four. We perform a detailed analysis of the 1/N -expansion in d = 3 and demonstrate full agreement with the conformal bootstrap. We argue that this is a useful starting point for more sophisticated computations of the critical indices.

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“…That this is indeed the case in d = 3 has only recently been proven using the renormalization group technique of constructive field theory [17].…”

Section: Introductionmentioning

confidence: 99%

Four-Fermion Theory and the Conformal Bootstrap

Chen¹,

Makeenko²,

Semenoff³

1993

Annals of Physics

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“…Regarding the first inclusion, we were surprised to find in the recent literature a combinatorial proof, with a flavor of loop-erased random walk, of the eminently classical Cayley-Hamilton theorem [37]. As for the second inclusion, there is a very nice explicit Fermionic proof [12] that, for a generic n × n matrix N, (tr N) k(n−1)+1 is in the ideal generated by the matrix elements of N k .…”

Section: Iii2 Chains And/or Loops?mentioning

confidence: 99%

“…Now algebraic combinatorialists might not be too impressed by this since one can readily rewrite formula (12) under the form given by Towber [40] or Singer [34]. So the series expansion of the formal inverse itself is not new.…”

Section: The Formal Inverse As a One-point Correlation Functionmentioning

confidence: 99%

The Jacobian Conjecture as a Problem of Perturbative Quantum Field Theory

Abdesselam¹

2003

Ann. Henri Poincaré

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“…It has also been argued [12]- [14] that the four dimensional Yukawa-φ 4 theory in 4 − ǫ dimensions represents the universality class of the Gross-Neveu model in dimensions between 2 and 4. The latter is also renormalizable only in the 1/N expansion [15,16] and the critical exponents have been computed to high order [17]- [19]. The O(N) model has one relevant coupling constant in the 4-dimensional theory, so the fixed point of order ǫ is automatically infrared stable and the phase transition is of second order.…”

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confidence: 99%

New Universality Classes for Quantum Critical Behavior

et al. 1995

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We use the epsilon expansion to explore a new universality class of second order quantum phase transitions associated with a four-dimensional Yukawa field theory coupled to a traceless Hermitean matrix scalar field. We argue that this class includes four-fermi models in 2 < D < 4 dimensions with SU (N F ) × U (N ) symmetry and a U (N ) scalar, SU (N F ) iso-vector 4-fermi coupling. The epsilon expansion indicates that there is a second order phase transition for N ≥ N * (N F ), where N * (N F ) ≃ .27N F if N F → ∞.

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Constructing the three-dimensional Gross-Neveu model with a large number of flavor components

Cited by 84 publications

References 13 publications

Four-Fermion Theory and the Conformal Bootstrap

Four-Fermion Theory and the Conformal Bootstrap

The Jacobian Conjecture as a Problem of Perturbative Quantum Field Theory

New Universality Classes for Quantum Critical Behavior

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