Logarithmic two-point scaling at a cubic asymptotically free beta function
= Logarithmic two-point scaling at a cubic asymptotically free beta function
{title2=$d(z,g)=d(1,\bar g)[1+bg^2\log z]^{c/b}$}
For $\beta=-bg^3$, $\gamma_\phi=cg^2$, and $b>0$, one has $\bar g^2=g^2/(1+bg^2\log z)$. Integrating the <field-renormalization anomalous dimension> gives the displayed logarithmic factor. At large $z$, a nonzero free matching factor yields $d\sim C(\log z)^{c/b}$ in the printed RG sign convention.