Bounds on the decay of the auto-correlation in phase ordering dynamics

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 limt2»t₁7lt; φ(r,t₁)φ(r,t₂)>~L (t₂)^-λ]. 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 t₁ = 0. If t₁ 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 t₁=0 or t₁»1. Our numerical simulations for the two-dimensional, conserved scalar order parameter show that λ?4 for t₁ in the scaling regime, consistent with our bound. The asymptotic decay when t₁=0, while exhibiting an unexpected sensitivity to the amplitude of the initial correlations, is slower than when t₁»1 and obeys the bound λ≥d/2.