Persistence, Poisoning, and Autocorrelations in Dilute Coarsening
arXiv:cond-mat/9707228 · doi:10.1103/PhysRevLett.79.4842
Abstract
We calculate the exact autocorrelation exponent lambda and persistence exponent theta, and also amplitudes, in the dilute limit of phase ordering for dimensions d >= 2. In the Lifshitz-Slyozov-Wagner limit of conserved order parameter dynamics we find theta = gamma_d*epsilon, a universal constant times the volume fraction. For autocorrelations, lambda = d at intermediate times, with a late time crossover to lambda >= d/2 + 2. We also derive lambda and theta for globally conserved dynamics and relate these to the q->infinity -state Potts model and soap froths, proposing new poisoning exponents.
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