Fluctuations and Criticality of a Granular Solid-Liquid-like Phase Transition

Details Fluctuations and Criticality of a Granular Solid-Liquid-like Phase Transition Fluctuations and Criticality of a Granular Solid-Liquid-like Phase Transition

2012-03-31

arxiv.org/abs/1204.0059v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures, submitted to Physical Review Letters

Scientific paper

We present an experimental study of density and order fluctuations in the vicinity of the solid-liquid-like transition that occurs in a vibrated quasi-two-dimensional granular system. We show that density fluctuations, characterized through the structure factor, increase in size and intensity as the transition is approached, but they do not change significantly at the transition itself. The dense, metastable clusters also increase their local order in the vicinity of the transition. This is characterized through the bond-orientational order parameter $Q_4$, which in Fourier space obeys an Ornstein-Zernike behavior. Depending on filling density and vertical height, the transition can be of first or second order type. In the latter case, the associated correlation length $\xi_4$, relaxation time $\tau_4$, zero $k$ limit of $Q_4$ fluctuations (static susceptibility), the pair correlation function of $Q_4$, and the amplitude of the order parameter obey critical power laws, with saturations due to finite size effects. Their respective critical exponents are $\nu_{\bot} = 1$, $\nu_{||} = 2$, $\gamma = 1$, $\eta=0.67$, and $\beta=1/2$, whereas the dynamical critical exponent $z = \nu_{||}/\nu_{\bot} = 2$. These results are consistent with model C of dynamical critical phenomena, valid for a non-conserved critical order parameter (bond-orientation order) coupled to a conserved field (density).

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