# Particle systems with weakly attractive interaction

September 14, 2004

Systems of classical continuous particles in the grand canonical ensemble
interacting through purely attractive, yet stable, interactions are defined. By
a lattice approximation, FKG ferromagnetic inequalities are shown to hold for
such particle systems. Using these inequalities, a construction of the infinite
volume measures is given by a monotonicity and upper bound argument. Invariance
under Euclidean transformations is proven for the infinite volume measures. The
construction works for arbitrary activity and temperature and for integrable
long range interactions. Also, inhomogeneous systems of particles with
different "charge" can be treated.

Keywords:

*none*