P Gonos and A J Bray 2005 J. Phys. A: Math. Gen. 38 1427 doi:10.1088/0305-4470/38/7/002
Persistence in systems with conserved order parameter
P Gonos and A J Bray
Show affiliationsWe 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) 
lγ with γ = −1. We generalize this model to arbitrary γ, and derive an expression for the domain density, N(t) ~ t−
with = 1/(2 − γ), using a scaling argument. We also investigate numerically the persistence exponent θ characterizing the power-law decay of the number, Np(t), of persistent (unflipped) spins at time t, and find Np(t) ~ t−θ where θ depends on γ. We show how the results for 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 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.
- PACS
- MSC
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82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
- Subjects
- Dates
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Issue 7 (18 February 2005)
Received 13 October 2004, in final form 16 December 2004
Published 2 February 2005
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Persistence in systems with conserved order parameter
P Gonos and A J Bray 2005 J. Phys. A: Math. Gen. 38 1427
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