Percolation Properties of the Non-ideal Gas

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.