Persistence in systems with conserved order parameter

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) ∝ l^γ with γ = −1. We generalize this model to arbitrary γ, and derive an expression for the domain density, N(t) ∼ t^−ϕ with ϕ = 1/(2 − γ), using a scaling argument. We also investigate numerically the persistence exponent θ characterizing the power-law decay of the number, N_p(t), of persistent (unflipped) spins at time t, and find N_p(t) ∼ t^−θ where θ depends on γ. We show how the results for ϕ and θ 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 ϕ is the same in both models, θ is different except for γ = 0. We also investigate models that interpolate between symmetric domain diffusion and DLCA.