Marek Biskup, Lincoln Chayes, Roman Kotecky
On the formation/dissolution of equilibrium droplets
(176K, PDF Document)

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.