Persistence, Poisoning, and Autocorrelations in Dilute Coarsening

TL;DR

This paper provides exact calculations of autocorrelation and persistence exponents in dilute phase ordering, revealing universal behaviors and new poisoning exponents in conserved dynamics across multiple models.

Contribution

It offers the first exact derivations of autocorrelation and persistence exponents in dilute coarsening, including universal constants and new poisoning exponents.

Findings

Autocorrelation exponent lambda equals the dimension d at intermediate times.

Persistence exponent theta is proportional to volume fraction with a universal constant.

Identifies crossover behaviors and relates exponents to models like Potts and soap froths.

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.