On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model

Abstract

We investigate whether the beta function of the finite-$N$ Gross-Neveu model, as calculated up to the four-loop level, exhibits evidence for an infrared zero. As part of our analysis, we calculate and analyze Padé approximants to this beta function and evaluate effects of scheme dependence. From our study, we find that in the range of coupling where the perturbative calculation of the four-loop beta function is reliable, it does not exhibit robust evidence for an infrared zero.

10 pages

References in corpus (12)

• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Infrared Zero of $\beta$ and Value of ${\gamma }_m$ for an SU(3) Gauge Theory at the Five-Loop Level
• Ising and Gross-Neveu model in next-to-leading order
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Conformal Behavior at Four Loops and Scheme (In)Dependence
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• Banks-Zaks fixed point analysis in momentum subtraction schemes
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• Study of the Six-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory

Cited by in corpus (5)

• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Momentum dependence of quantum critical Dirac systems
• Quantum Simulation of the N flavor Gross-Neveu Model
• Renormalization group analysis of Dirac fermions with random mass
• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions