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A magnetic system with a phase transition at temperature $T_c$ may exhibitdouble resonance peaks under a periodic external magnetic field because thetime scale matches the external frequency at two different temperatures, oneabove $T_c$ and the other below $T_c$. We study the double resonance phenomenafor the mean-field $q$-state clock model based on the heat-bath-typed masterequation. We find double peaks as observed in the kinetic Ising case ($q=2$)for all $q\ge 4$, but for the three-state clock model ($q=3$), the existence ofdouble peaks is possible only above a certain external frequency since itundergoes a discontinuous phase transition.

Double stochastic resonance in the mean-field $q$-state clock models