On the formation/dissolution of equilibrium droplets

Abstract

We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $δN$ of particles above the ambient gas density. We identify a dimensionless parameter $Δ\sim(δN)^{(d+1)/d}/V$ and a \textrm{universal} value $\Deltac=\Deltac(d)$, and show that a droplet of the dense phase occurs whenever $Δ>\Deltac$, while, for $Δ<\Deltac$, the excess is entirely absorbed into the gaseous background. When the droplet first forms, it comprises a non-trivial, \textrm{universal} fraction of excess particles. Similar reasoning applies to generic two-phase systems at phase coexistence including solid/gas--where the ``droplet&#39;&#39; is crystalline--and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.