Persistence and life time distribution in coarsening phenomena

We investigate the lifetime distribution P(τ,t) in one and two dimensional coarsening processes modelled by Ising–Glauber dynamics at zero temperature. The lifetime τ is defined as the time that elapses between two successive flips in the time interval (0,t) or between the last flip and the observation time t. We calculate P(τ,t) averaged over all the spins in the system and over several initial disorder configurations. We find that asymptotically the lifetime distribution obeys a scaling ansatz: P(τ,t)=t−1φ(ξ), where ξ=τ/t. The scaling function φ(ξ) is singular at ξ=0 and 1, mainly due to slow dynamics and persistence. An independent lifetime model where the lifetimes are sampled from a distribution with power law tail is presented, which predicts analytically the qualitative features of the scaling function. The need for going beyond the independent lifetime models for predicting the scaling function for the Ising–Glauber systems is indicated.