On the equivalence between 2D Yukawa and Gross-Neveu models

Focht, E.; Franzki, W.; Jersák, J.; Stephanov, Mikhail

doi:10.1016/0550-3213(94)00304-1

Cited by 3 publications

(3 citation statements)

References 29 publications

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“…This satisfies the condition Λ ≫ m. The condition ξ ≫ 1, or ma = 1/ξ → 0, specifies a 2-dimensional critical surface in the space of 3 parameters κ, λ lat and β. One expects that a continuum limit taken at any generic point of this surface defines the same theory [5,10]. (This is the meaning of the equivalence between Yukawa and four-fermion theories).…”

Section: Lattice Theorymentioning

confidence: 99%

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Critical region of the finite temperature chiral transition

1998

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We study a Yukawa theory with spontaneous chiral symmetry breaking and with a large number N of fermions near the finite temperature phase transition. Critical properties in such a system can be described by the mean field theory very close to the transition point. We show that the width of the region where non-trivial critical behavior sets in is suppressed by a certain power of 1/N. Our Monte Carlo simulations confirm these analytical results. We discuss implications for the chiral phase transition in QCD.Comment: 18 page

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Section: Lattice Theorymentioning

confidence: 99%

“…The action is that of the Yukawa lattice theory (7) with κ = λ = 0, and we tuned β to reach criticality. The long-wavelength (continuum limit) behavior of such a theory is determined by the infrared fixed point, which is the same [5,10] in the more general Yukawa model (7) and in the Gross-Neveu model.…”

Section: Monte Carlomentioning

confidence: 99%

Critical region of the finite temperature chiral transition

1998

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“…This Yukawa term identifies the direction of a "renormalised trajectory" (a line of perfect actions in parameter space) emanating from the critical surface. 28 The corresponding couplings in coordinate space can be evaluated numerically, and they have been applied -in a truncated form -in lattice simulations [69].…”

Section: )mentioning

confidence: 99%

Optimised Dirac operators on the lattice: construction, properties and applications

Bietenholz

2008

Fortschritte der Physik

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We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the -regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian -the chiral condensate and the pion decay constant -from QCD simulations with extremely light quarks. Motivation and overviewOver the recent decades quantum field theory has been established as the appropriate formalism for particle physics, as far as it is explored experimentally. Its treatment by perturbation theory led to successful results, for instance in Quantum Electrodynamics (QED), in the electroweak sector of the Standard Model and in Quantum Chromodynamics (QCD) at high energy. However, there are still many open questions, which require results at finite coupling strength -beyond the range of perturbation theory -such as numerous aspects of QCD at low and moderate energy.A method is known which has the potential to provide fully non-perturbative results for a number of field theoretic questions. This method applies Monte Carlo simulations to lattice regularised quantum field theories. The generic uncertainty of perturbation theory -uncontrolled contributions beyond the calculated order -disappears in this approach. However, one has to deal with statistical errors, as well as ambiguities in the extrapolation to the continuum and to a large volume.Simulation results are obtained at finite lattice spacing, which causes systematic artifacts in the numerically measured observables. The stability of dimensionless ratios of observables under the variation of the lattice spacing is denoted as the scaling behaviour. Its quality, which is vital for the reliability of the continuum extrapolation, depends on the way in which the lattice regularisation is implemented. This work deals * www.fp-journal.org Fortschr. Phys. 56, No. 2 (2008) 109For practical applications, i.e. for the applicability in simulations, the couplings have to be truncated. In Sect. 6 we describe our truncation scheme for the perfect fermion to a so-called hypercube fermion, which has been simulate...

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Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories

Franzki¹,

Jersák

Welters³

1996

Phys. Rev. D

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We generalize the N F ϭ2 Schwinger model on the lattice by adding a charged scalar field. In this so-called U 2 model the scalar field shields the fermion charge, and a neutral fermion, acquiring mass dynamically, is present in the spectrum. We study numerically the mass of this fermion at various large fixed values of the gauge coupling by varying the effective four-fermion coupling, and find an indication that its scaling behavior is the same as that of the fermion mass in the chiral Gross-Neveu model. This suggests that the U 2 model is in the same universality class as the Gross-Neveu model, and thus renormalizable and asymptotic-free at arbitrary strong gauge coupling. The model illustrates that strongly coupled gauge theories might provide an alternative to the Higgs mechanism of mass generation. ͓S0556-2821͑96͒00124-5͔

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On the equivalence between 2D Yukawa and Gross-Neveu models

Cited by 3 publications

References 29 publications

Critical region of the finite temperature chiral transition

Critical region of the finite temperature chiral transition

Optimised Dirac operators on the lattice: construction, properties and applications

Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories

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