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arXiv · 0903.0841

Percolation properties of non-ideal gas

E. Pechersky·A. Yambartsev
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Abstract

We estimate locations of the regions of the percolation and of the non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our results about the percolation and about the non-percolation are obtained under different assumptions. The intersection of two groups of the assumptions reduces the results to two dimension Euclidean space, $\R^2$, and to a potential function of the interactions having a hard core. The technics for the percolation proof is based on a contour method which is applied to a discretization of the Euclidean space. The technics for the non-percolation proof is based on the coupling of the Gibbs field with a branching process.

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E. Pechersky, A. Yambartsev. 2009-03-04. Percolation properties of non-ideal gas. https://doi.org/10.1007/s10955-009-9856-4

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