On the formation/dissolution of equilibrium droplets

We consider liquid-vapor systems in finite-volume V subset of R(d) at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess deltaN of particles above the ambient gas density. We identify a dimensionless parameter Delta similar to (deltaN)((d + 1)/d) /V and a universal value Delta(c) = Delta(c)(d), and show that a droplet of the dense phase occurs whenever Delta > Delta(c), while, for Delta < Delta(c), the excess is entirely absorbed into the gaseous background. When the droplet first forms, it comprises a non-trivial, universal fraction of excess particles. Similar reasoning applies to generic two-phase systems at phase coexistence including solid/gas-where the droplet is crystalline and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.