Universality of ordering dynamics in conserved multicomponent systems

Abstract

A comparative study is performed of the ordering dynamics and spinodal decomposition processes in two-dimensional two-state and three-state ferromagnetic Potts models with conserved order parameter. The models are investigated by Monte Carlo quenching simulations on both square and triangular lattices and the evolving order is studied via the excess energy, the domain-size distribution function, and the density of isolated diffusing particles, which facilitate the coarsening process. The growth law that describes the time-evolution of the linear length scale, R(t), of the ordered domains is found at late stages to be algebraic, R(t)∼${\mathit{t}}^{\mathit{n}}$, with the Lifshitz-Slyozov value of the exponent, n≃1/3, for both two- and three-component order parameters. The domain-size distribution function is found to obey dynamical scaling. The results suggest that, similar to the case of nonconserved order parameter, there is a single universality class describing the cases of conserved order parameter independent of the number of components of the order parameter. In the asymptotic regime, the topological difference in the domain-boundary network between the vertex-free two-state model and the vertex-generating three-state model does not affect the growth exponents but only the nonuniversal amplitudes. Details are revealed of the ordering mechanism controlled by diffusional processes involving broken Potts bonds and isolated Potts spins. A transient regime can be identified as one where broken Potts bonds in the two-state model and broken Potts bonds (isolated Potts) spins in the three-state model diffuse along the domain boundaries and an asymptotic late-stage regime where isolated Potts spins perform a long-range diffusive process within and across the domains.