Persistence, Poisoning, and Autocorrelations in Dilute Coarsening

We calculate the exact autocorrelation exponent $\lambda$ and persistence exponent $\theta$, and also amplitudes, in the dilute limit of phase ordering for dimensions $d\ge 2$. 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 $\lambda \ge d/2+2$. We also derive $\lambda$ and $\theta$ for globally conserved dynamics and relate these to the $q\to \infty$–state Potts model and soap froths, proposing new poisoning exponents.