02-305 Marek Biskup, Lincoln Chayes, Roman Kotecky
On the formation/dissolution of equilibrium droplets (176K, PDF Document) Jul 9, 02
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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 $\delta N$ of particles above the ambient gas density. We identify a dimensionless parameter $\Delta\!\sim\!(\delta N)^{(d+1)/d}/V$ and a \textrm{universal} value $\Deltac=\Deltac(d)$, and show that a droplet of the dense phase occurs whenever $\Delta\!>\!\Deltac$, while, for~$\Delta\!<\!\Deltac$, 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'' is crystalline---and polymorphic~systems. A sketch of a rigorous proof for the 2D~Ising lattice gas is presented; generalizations are discussed heuristically.

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