Percolation properties of non-ideal gas

TL;DR

This paper investigates the conditions under which a non-ideal gas exhibits percolation or non-percolation in a two-dimensional Euclidean space, using contour and coupling techniques.

Contribution

It provides new criteria for percolation and non-percolation in interacting particle systems with hard core potentials, under different assumptions.

Findings

Identifies regions in parameter space where percolation occurs.

Establishes conditions for non-percolation using coupling methods.

Applies contour methods to discretized Euclidean space.

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.