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

TL;DR

This paper investigates the phase-ordering dynamics of non-conserved O(n) models without topological defects using simulations and analytical methods, revealing a stretched exponential tail in the structure factor and scaling behavior.

Contribution

It provides new insights into the structure-factor tail and asymptotic behavior for non-conserved fields without topological defects, extending previous simulation results with analytical analysis.

Findings

Dynamical scaling with length L(t) = t^{1/2} observed.

Structure-factor tail fits a stretched exponential form.

Asymptotic behavior matches analytical large-N approximation.

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 $g(q)\sim \exp(-bq^\delta)$, 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.