Dynamic modes of active Potts models with factorizable numbers of states

We studied the long-term nonequilibrium dynamics of $q$-state Potts models with $q=4$, $5$, $6$, and $8$ using Monte Carlo simulations on a two-dimensional square lattice. When the contact energies between the nearest neighbors for the standard Potts models are used, cyclic changes in the $q$ homogeneous phases and $q$-state coexisting wave mode appear at low and high flipping energies, respectively, for all values of $q$. However, for a factorizable $q$ value, dynamic modes with skipping states emerge, depending on the contact energies. For $q=6$, a spiral wave mode with three domain types (one state dominant or two states mixed) and cyclic changes in three homogeneous phases are found. Although three states can coexist spatially under thermal equilibrium, the scaling exponents of the transitions to the wave modes are modified from the equilibrium values.