We calculate the exact autocorrelation exponent λ and persistence exponent θ, 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 θ0ex0ex=0ex0exγdε, a universal constant times the volume fraction. For autocorrelations, λ0ex0ex=0ex0exd at intermediate times, with a late time crossover to λ≥d/2+2. We also derive λ and θ for globally conserved dynamics and relate these to the q→∞--state Potts model and soap froths, proposing new poisoning exponents.
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Lee et al. (1997) studied this question.
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