Persistence, Poisoning, and Autocorrelations in Dilute Coarsening

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  • 22 July 1997
Abstract
We derive exact expressions for the autocorrelation exponent lambda and the persistence exponent theta, and also amplitudes, in the dilute limit of conserved phase ordering for dimensions d >= 2. These represent the first exact results for theta in T < T_c coarsening. In the Lifshitz-Slyozov-Wagner limit of conserved order parameter dynamics, theta is given by a universal constant times the volume fraction, theta = gamma_d epsilon. For autocorrelations, lambda = d at early times, with a crossover to lambda >= d/2+2 when drops have grown larger than their earlier drop spacing. We also derive lambda and theta for a globally conserved order parameter in the small volume fraction limit and relate these results to the q -> infinity-state Potts model and soap froths, proposing new poisoning exponents.

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