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

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