  We establish new scaling properties for the universality class of Model C,
which describes relaxational critical dynamics of a nonconserved order
parameter coupled to a conserved scalar density. We find an anomalous diffusion
phase, which satisfies weak dynamic scaling while the conserved density
diffuses only asymptotically. The properties of the phase diagram for the
dynamic critical behavior include a significantly extended weak scaling region,
together with a strong and a decoupled scaling regime. These calculations are
done directly in 2 < d < 4 space dimensions within the framework of the
nonperturbative functional renormalization group. The scaling exponents
characterizing the different phases are determined along with subleading
indices featuring the stability properties.
