  We give a new criterion for a classical gas with a repulsive pair potential
to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of
the pressure. Our improvement on the bound for analyticity is by a factor $e^2$
over the classical cluster expansion approach and a factor $e$ over the known
limit of cluster expansion convergence. The criterion is based on a contractive
property of a recursive computation of the density of a point process. The key
ingredients in our proofs include an integral identity for the density of a
Gibbs point process and an adaptation of the algorithmic correlation decay
method from theoretical computer science. We also deduce from our results an
improved bound for analyticity of the pressure as a function of the density.
