Two-point scaling at an ultraviolet fixed point ($G(p)\propto (p^2{)}^{-1+{\gamma }_{\ast }}$)

If $g(t)\to g_{\ast }$, $\gamma (g(t))\to {\gamma }_{\ast }$ and the reference correlator has a finite nonzero fixed-point limit, the characteristic solution of the multiplicative Callan-Symanzik equation gives $\log f(t)=2{\gamma }_{\ast }t+o(t)$. A simple attractive fixed point and smooth anomalous dimension give a finite prefactor multiplying $e^{2{\gamma }_{\ast }t}$. A nonsimple fixed point can retain slower corrections.