Study of the Question of an Ultraviolet Zero in the Six-Loop Beta Function of the O($N$) $\lambda |\vec{\varphi }{|}^4$ Theory

Abstract

We study the possibility of an ultraviolet (UV) zero in the six-loop beta function of an O($N$) $\lambda |\vec{\varphi }{|}^4$ field theory in $d=4$ spacetime dimensions. For general $N$, in the range of values of $\lambda$ where a perturbative calculation is reliable, we find evidence against such a UV zero in this six-loop beta function.

arXiv comment15 pages, 1 figure

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Cited by in corpus (7)

• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Phase transition of four-dimensional lattice ${\varphi }^4$ theory with tensor renormalization group
• Effect of Scheme Transformations on a Beta Function with Vanishing One-Loop Term
• Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions
• The $O(4)$ ${\varphi }^4$ model as an effective light meson theory: A lattice-continuum comparison