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

TL;DR

This paper derives bounds on the decay exponent of autocorrelation functions in phase ordering, revealing differences based on conservation laws and initial conditions, supported by numerical simulations.

Contribution

It establishes new bounds on the autocorrelation decay exponent for conserved and non-conserved order parameters, and compares these with numerical results.

Findings

For non-conserved order parameter, lambda >= d/2.

For conserved order parameter, lambda >= d/2 + 2 in the scaling regime for t1 > 0.

Numerical simulations show lambda approx 3 for t1=0 and lambda approx 4 for t1 >> 1 in 2D.

Abstract

We obtain bounds on the decay exponent lambda of the autocorrelation function in phase ordering dynamics. For non-conserved order parameter, we recover the Fisher and Huse inequality, lambda > = d/2. If the order parameter is conserved we also find lambda >= d/2 if the initial time t1 = 0. However, for t1 in the scaling regime, we obtain lambda >= d/2 + 2 for d >= 2 and lambda >= 3/2 for d=1. For the one-dimensional scalar case, this, in conjunction with previous results, implies that lambda is different for t1 = 0 and t1 >> 1. In 2-dimensions, our extensive numerical simulations for a conserved scalar order parameter show that lambda approx 3 for t1=0 and lambda approx 4 for t1 >> 1. These results contradict a recent conjecture that conservation of order parameter requires lambda = d. Quenches to and from the critical point are also discussed. (uuencoded PostScript file with figures appended at end).