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Percolation Properties of the Non-ideal Gas

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Abstract

We estimate locations of the regions of the percolation and of the non-percolation in the plane (λ,β): the Poisson rate–the inverse temperature, for interacting 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, ℝ2, 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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Authors and Affiliations

  1. IITP, 19, Bolshoj Karetny per., Moscow, Russia

    E. Pechersky

  2. IME-USP, Rua do Matão, 1010, 05508-090, São Paulo, Brazil

    A. Yambartsev

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  1. E. Pechersky
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  2. A. Yambartsev
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Correspondence to E. Pechersky.

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Pechersky, E., Yambartsev, A. Percolation Properties of the Non-ideal Gas. J Stat Phys 137, 501–520 (2009). https://doi.org/10.1007/s10955-009-9856-4

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  • DOI: https://doi.org/10.1007/s10955-009-9856-4

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