On the formation/dissolution of equilibrium droplets

Details On the formation/dissolution of equilibrium droplets On the formation/dissolution of equilibrium droplets

2002-07-10

arxiv.org/abs/math-ph/0207012v1

Europhys. Lett. 60:1 (2002) 21-27

Physics

Mathematical Physics

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

Scientific paper

10.1209/epl/i2002-00312-y

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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