BOUNDS ON THE DECAY OF THE AUTOCORRELATION IN PHASE ORDERING DYNAMICS

We investigate the decay of temporal correlations in phase ordering dy namics by obtaining bounds on the decay exponent lambda of the autocor relation function [defined by lim(t2 much greater than t1) [phi(r,t(1) )phi(r,t(2))]similar to L(t(2))(-lambda)]. For a nonconserved order pa rameter, we recover the Fisher and Huse inequality, lambda greater tha n or equal to d/2. For a conserved order parameter, we find lambda gre ater than or equal to d/2 only if t(1) = 0. If t(1) is in the scaling regime, then lambda greater than or equal to d/2+2 for d greater than or equal to 2 and lambda 3/2 for d=1. For the one-dimensional scalar c ase, this, in conjunction with previous results, implies that the valu e of lambda depends on whether t(1)=0 or t(1) much greater than 1. Our numerical simulations for the two-dimensional, conserved scalar order parameter show that lambda approximate to 4 for t(1) in the scaling r egime, consistent with our bound. The asymptotic decay when t(1)=0, wh ile exhibiting an unexpected sensitivity to the amplitude of the initi al correlations, is slower than when t(1) much greater than 1 and obey s the bound lambda greater than or equal to d/2.