Structure-Factor Tail for the Ordering Kinetics of Nonconserved Fields without Topological Defects

Abstract

Using a cell dynamic system (CDS) simulation scheme, we investigate the phase-ordering dynamics of non-conserved O(n) models without topological defects, i.e. for $n>d+1$ where $d$ is the spatial dimensionality. In particular, we consider zero-temperature quenches for $d=2$, $n=4,5$, and for $d=1$, $n=3,4,5$. We find, in agreement with previous simulations using fixed-length spins, that dynamical scaling is obtained, with characteristic length $L(t)=t^{1/2}$. We show that the asymptotic behaviour of the structure-factor scaling function $g(q)$ is well fitted by the stretched exponential form $g(q)\sim \exp (-b{q}^{\delta })$, with an exponent $\delta$ that appears to depend on both n and d. An analytical treatment of an approximate large-N equation for the pair correlation function yields $g(q)\sim q^{-(d-1)/2}\exp (-bq)$, with $b\sim (\ln n{)}^{1/2}$ for large $n$, in agreement with recent simulations of the same equation.

Latex, 22 pages, 10 figures

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Cited by in corpus (1)

• Overall time evolution in phase-ordering kinetics