One-loop quartic scalar beta function
= One-loop quartic scalar beta function
{title2=$\beta(\lambda)=3\lambda^2/(16\pi^2)+O(\lambda^3)$}
With interaction $\lambda\phi^4/4!$ for one real scalar, the three one-loop four-point bubble channels give the four-dimensional <renormalization-group beta function> $\beta(\lambda)=3\lambda^2/(16\pi^2)+O(\lambda^3)$. Its positive sign for $\lambda>0$ excludes <asymptotic freedom> and produces a perturbative <Landau pole> on extrapolation.