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

Order parameter scaling in fluctuation dominated phase ordering