Tricritical sextic beta function ($d\lambda /ds=-C{\lambda }^2+\cdots$)

In three dimensions, after tuning the quadratic and quartic relevant operators, the positive sextic coupling has a renormalization-group beta function $d\lambda /ds=-C{\lambda }^2+\cdots$ with $C>0$ for increasing length scale $s$. The Wick contractions connecting two sextic vertices with three propagators give the primitive logarithmic correction. The interaction is marginally irrelevant.