Coarsening dynamics for spiral and nonspiral waves in active Potts models

Abstract: 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. When spiral waves appear in the final state, the correlation length follows the Lifshitz--Allen--Cahn (LAC) law ($\propto t^{1/2}$) until saturation is observed at the characteristic wavelength. By contrast, in the case of nonspiral waves, the growth rate is raised prior to the saturation, leading to a transient increase in the coarsening exponent. Moreover, the mean cluster size exhibits a similar form of transient increase under most of the conditions. In factorized symmetry modes at $q=6$, domains composed of two or three states similarly follow the LAC law. Finally, this study confirmed that the choice of lattice type (square or hexagonal) and update scheme (Metropolis or Glauber) does not alter the dynamic behavior.