Bounds on the decay of the autocorrelation in phase ordering dynamics.

We obtain bounds on the decay exponent λ of the autocorrelation function in phase ordering dynamics (defined by limt2≫t1〈φ(r, t1)φ(r, t2)〉 ∼ L(t2)). For non-conserved order parameter, we recover the Fisher and Huse inequality, λ ≥ d/2. If the order parameter is conserved we also find λ ≥ d/2 if t1 = 0. However, for t1 in the scaling regime, we obtain 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 λ is different for t1 = 0 and t1 ≫ 1. In 2-dimensions, our extensive numerical simulations for a conserved scalar order parameter show that λ ≈ 3 for t1 = 0 and λ ≈ 4 for t1 ≫ 1. These results contradict a recent conjecture that conservation of order parameter requires λ = d. Quenches to and from the critical point are also discussed. PACS: 64.60.My, 68.35.Fx Typeset using REVTEX