  We develop a dynamic field-theoretic renormalization-group (RG) theory for
the cooling first-order phase transitions in the Potts model. It is suggested
that the well-known imaginary fixed points of the $q$-state Potts model for
$q>10/3$ in the RG theory are the origin of the dynamic scaling found recently,
apart from the logarithmic corrections. This indicates that the real and
imaginary fixed points of the Potts model are both physical and control the
scalings of the continuous and discontinuous phase transitions, respectively,
of the model. Our one-loop results for the scaling exponents are already not
far away from the numerical results. Further, the scaling exponents depend on
$q$ slightly only, in consistence with the numerical results. Therefore, the
theory is believed to provide a natural explanation of the dynamic scaling
including the scaling exponents and their scaling laws for various observables
in the Potts model.
