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.

arXiv comment10 pages

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Cited by in corpus (10)

• Higher-Order Scheme-Independent Series Expansions of ${\gamma }_{\bar{\psi }\psi ,IR}$ and ${\beta }_{IR}^{\prime }$ in Conformal Field Theories
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• 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
• A critical look at $\beta$-function singularities at large $N$
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Renormalization group analysis of Dirac fermions with random mass
• Bubble-resummation and critical-point methods for $\beta$-functions at large $N$
• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions