On the formation/dissolution of equilibrium droplets

Abstract

We consider liquid-vapor systems in finite volume $V\subset {\mathbb{R}}^d$ 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 $Δ>\Deltac$, 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'' is crystalline--and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.

An announcement of a forthcoming rigorous work on the 2D Ising model; to appear in Europhys. Lett

References in corpus (3)

• Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
• Crossing the coexistence line at constant magnetization
• Droplets in the coexistence region of the two-dimensional Ising model

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