Coarsening dynamics for spiral and disordered waves in active Potts models

This study examines the domain-growth dynamics of $q$-state active Potts models ($q=3$--$8$) under the cyclically symmetric conditions using Monte Carlo simulations on square and hexagonal lattices. By imposing active cyclic flipping of states, finite-length waves emerge in the long-term limit. This study focuses on coarsening dynamics from an initially random mixture of states to these moving-domain states. The correlation length and mean cluster size grow, following the Lifshitz--Allen--Cahn (LAC) law ($\propto t^{1/2}$) in the intermediate time range, and in the late range, saturation is observed at the characteristic wavelengths. It is found that the growth rate is raised prior to saturation, leading to a transient increase in the coarsening exponent. The coarsening dynamics to disordered waves exhibit greater transient increases than those to spiral waves. Moreover, the transient increase is greater at higher $q$. In factorized symmetry modes at $q=6$, domains composed of two or three states similarly follow the LAC law. Finally, this study confirms that the choice of lattice type (square or hexagonal) and update scheme (Metropolis or Glauber) does not alter the dynamic behavior.