Order parameter scaling in fluctuation dominated phase ordering

TL;DR

This paper investigates the scaling behavior of multiple order parameters in fluctuation-dominated phase ordering systems, revealing distinct static and dynamic scaling laws for Fourier modes under different surface evolutions.

Contribution

It introduces a comprehensive analysis of order parameter scaling in fluctuation-dominated phase ordering, emphasizing the necessity of multiple Fourier components and characterizing their static and dynamic scaling laws.

Findings

Mean Fourier mode scales as L^{- ext{exponent}} with different exponents for EW and KPZ.

Scaling functions describe the probability distributions and correlation functions of Fourier modes.

Temporal intermittency and divergence of flatness are observed in the coarse-grained depth model.

Abstract

In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles (SP) on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavelength Fourier components of the density profile. We study both static and dynamic scaling laws obeyed by the Fourier modes $Q_m$ and find that the mean value obeys the static scaling law $\langle Q_m \rangle \sim L^{-\phi}f(m/L)$ with $\phi\simeq2/3$ and $\phi \simeq 3/5$ with Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surface evolution respectively. The full probability distribution $P(Q_m)$ exhibits scaling as well. Further, time-dependent correlation functions such as the steady state auto-correlation and cross-correlations of order parameter components are scaling functions of $t/L^z$, where $L$ is the system size and $z$ is the dynamic exponent with $z=2$ for EW and $z=3/2$ for KPZ surface evolution. In addition we find that the CD model shows temporal intermittency, manifested in the dynamical structure functions of the density and a weak divergence of the flatness as the scaled time approaches zero.