Uniqueness and absence of percolation of classical gases

Abstract

We reconsider Mürmann’s theorem, i.e., the 1-1 correspondence between Poisson exclusion finite-cluster processes and subcritical stable Gibbs processes of finite range. Subcritical processes realize configurations that decompose into only finite clusters. Existence or uniqueness of Poisson exclusion cluster processes then imply the corresponding statement for subcritical, stable Gibbs processes of finite range. Applications to continuum Potts models are given.