Percolation cluster statistics of 2D Lennard-Jones phases

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Abstract
The percolation cluster characteristics of 2D Lennard-Jones (LJ) fluid and solid phases have been determined by molecular dynamics computer simulation. The variation of the percolation threshold with temperature from the soft-core to hard-core limits is reported and interpreted in terms of changes in the short-range structure. The distribution of clusters is analysed using the cluster number distribution function, ns. Based in the small systems considered, the authors find that at the percolation threshold, the measured percolation exponent tau departs from the universal 2D value of 2.05, ranging from 1.6+or-0.1 in the soft-core limit to 2.0+or-0.05 in the hard-core limit. However, the fractal dimension of the clusters, Df, at the percolation threshold is indistinguishable from the 2D universal value of 1.9, having the range 1.9+or-0.1 for all state points considered. The same trends are observed in 3D LJ fluids. They examine the time dependence of the percolating clusters and show them to be ephemeral on a molecular timescale.