Disentangling growth and decay of domains during phase ordering

Using Monte Carlo simulations we study phase-ordering dynamics of a multispecies system modeled via the prototype q-state Potts model. In such a multispecies system, we identify a spin state or species as the winner if it has survived as the majority in the final state, otherwise, we mark them as loser. We disentangle the time (t) dependence of the domain length of the winner from losers, rather than monitoring the average domain length obtained by treating all spin states or species alike. The kinetics of domain growth of the winner at a finite temperature in space dimension d=2 reveal that the expected Lifshitz-Cahn-Allen scaling law ∼t^{1/2} can be realized with no early-time corrections, even for system sizes much smaller than what is traditionally used. Up to a certain period, all others species, i.e., the losers, also show a growth that, however, is dependent on the total number of species, and slower than the expected ∼t^{1/2} growth. Afterwards, the domains of the losers start decaying with time, for which our numerical data appear to be consistent with a ∼t^{-2} behavior. We also demonstrate that this approach of looking into the kinetics even provides new insights for the special case of phase ordering at zero temperature, both in d=2 and d=3.