Logarithmic two-point scaling from a cubic beta function
= Logarithmic two-point scaling from a cubic beta function
{title2=$g(t)=g(0)/\sqrt{1+2bg(0)^2t},\quad f(t)=(1+2bg(0)^2t)^{c/b}$}
For $\beta=-bg^3$ and $\gamma=cg^2$, 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.