Bounds on the decay of the autocorrelation in phase ordering dynamics

Chuck Yeung, Madan Rao, Rashmi C. Desai

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Abstract

We investigate the decay of temporal correlations in phase ordering dynamics by obtaining bounds on the decay exponent λ of the autocorrelation function [defined by [Formula Presented]〈φ(r,[Formula Presented])φ(r,[Formula Presented])〉∼L ([Formula Presented][Formula Presented]]. For a nonconserved order parameter, we recover the Fisher and Huse inequality, λ≥d/2. For a conserved order parameter, we find λ≥d/2 only if [Formula Presented] = 0. If [Formula Presented] is in the scaling regime, then λ≥d/2+2 for d≥2 and λ≥3/2 for d=1. For the one-dimensional scalar case, this, in conjunction with previous results, implies that the value of λ depends on whether [Formula Presented]=0 or [Formula Presented]≫1. Our numerical simulations for the two-dimensional, conserved scalar order parameter show that λ≊4 for [Formula Presented] in the scaling regime, consistent with our bound. The asymptotic decay when [Formula Presented]=0, while exhibiting an unexpected sensitivity to the amplitude of the initial correlations, is slower than when [Formula Presented]≫1 and obeys the bound λ≥d/2.

Original languageEnglish (US)
Pages (from-to)3073-3077
Number of pages5
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number4
DOIs
StatePublished - 1996

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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