= Nonzero ultraviolet fixed point of a cubic-quintic beta function
{title2=$\beta(g)=Bg^3-Ag^5,\quad g_*^2=B/A$}
For $A,B>0$, the nonzero zero of the <renormalization-group beta function> has slope $\beta^{\prime}(g_*)=-2B^2/A<0$ and is ultraviolet attractive. The origin is infrared attractive. A fixed-point <field-renormalization anomalous dimension> gives a power-law <quantum field theory propagator> factor $d(z)\sim Cz^{\gamma_\phi(g_*)}$. A weak fixed point is needed for control by a perturbative truncation.
Back to article page
