Cluster-size distributions in a classical many-body system

(Joint work with Sabine Jansen and Bernd Metzger)

We consider a classical many-body system in $\R^d$ with Lennard-Jones-type pair interaction, i.e., with prevention of clumping of the particles and with a preference of a certain positive distance for each pair of particles. We consider the free energy of the canonical ensemble in the thermodynamic limit and derive interesting emerging pictures when taking afterwards the coupled limit of high temperature and low density. It turns out that the particles unite in groups of one particular cardinality, the same everywhere in the system. Our methods are a comparison to an idealised model and a Gamma-convergence for the rate function of a characteristic large-deviation principle.