We develop a dynamic field-theoretic renormalization-group (RG) theory forthe cooling first-order phase transitions in the Potts model. It is suggestedthat 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 andimaginary fixed points of the Potts model are both physical and control thescalings of the continuous and discontinuous phase transitions, respectively,of the model. Our one-loop results for the scaling exponents are already notfar away from the numerical results. Further, the scaling exponents depend on$q$ slightly only, in consistence with the numerical results. Therefore, thetheory is believed to provide a natural explanation of the dynamic scalingincluding the scaling exponents and their scaling laws for various observablesin the Potts model.
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