Logarithmic two-point scaling from a cubic beta function ($g(t)=g(0)/\sqrt{1+2bg(0{)}^{2}t},f(t)=(1+2bg(0{)}^{2}t{)}^{c/b}$)

For $\beta =-b{g}^3$ and $\gamma =c{g}^2$, integrate the running coupling equation and then the anomalous-dimension multiplier. The correlator correction grows as a power $c/b$ of the logarithm of energy, rather than as a fixed power of energy. Higher perturbative orders change subleading terms while retaining this leading logarithmic exponent.