Continuum percolation for Gibbsian point processes with attractive interactions

Abstract

We study the problem of continuum percolation in infinite volume Gibbs measures for particles with an attractive pair potential, with a focus on low temperatures (large $\beta$). The main results are bounds on percolation thresholds ${\rho }_{\pm }(\beta )$ in terms of the density rather than the chemical potential or activity. In addition, we prove a variational formula for a large deviations rate function for cluster size distributions. This formula establishes a link with the Gibbs variational principle and a form of equivalence of ensembles, and allows us to combine knowledge on finite volume, canonical Gibbs measures with infinite volume, grand-canonical Gibbs measures.

22 pages. Corrected a statement on lattice gases, added reference

References in corpus (1)

• Abstract cluster expansion with applications to statistical mechanical systems