Persistence in systems with conserved order parameter

Abstract

We consider the low-temperature coarsening dynamics of a one-dimensional Ising ferromagnet with conserved Kawasaki-like dynamics in the domain representation. Domains diffuse with size-dependent diffusion constant, $D(l)\propto l^{\gamma }$ with $\gamma =-1$. We generalize this model to arbitrary $\gamma$, and derive an expression for the domain density, $N(t)\sim t^{-\varphi }$ with $\varphi =1/(2-\gamma )$, using a scaling argument. We also investigate numerically the persistence exponent $\theta$ characterizing the power-law decay of the number, $N_p(t)$, of persistent (unflipped) spins at time $t$, and find $N_p(t)\sim t^{-\theta }$ where $\theta$ depends on $\gamma$. We show how the results for $\varphi$ and $\theta$ are related to similar calculations in diffusion-limited cluster-cluster aggregation (DLCA) where clusters with size-dependent diffusion constant diffuse through an immobile `empty' phase and aggregate irreversibly on impact. Simulations show that, while $\varphi$ is the same in both models, $\theta$ is different except for $\gamma =0$. We also investigate models that interpolate between symmetric domain diffusion and DLCA.

9 pages, minor revisions