Theory of the evaporation /condensation transition of equilibrium droplets in finite volumes

A phenomenological theory of phase coexistence of finite systems near the coexistence curve that occurs in the thermodynamic limit is formulated for the generic case of d-dimensional ferromagnetic Ising lattices of linear dimension L with magnetization in slightly less than m(coex). It is argued that in the limit L --> infinity an unconventional first-order transition occurs at a characteristic value m(1) < M-coex, where a large equilibrium droplet ceases to exist, and the thermodynamically conjugate variable to m, the magnetic field H, exhibits a jump from H-t((1)) to H-t((2)). It is found that H-t((1.2)) scale like L-d/(d+1) their ratio being simply H-t((1))/H-t((2)) = (d+1)/(d-1), and m(coex) - m(t) infinity L-d/(d+1) as well, while the excess thermodynamic potential (relative to its value according to the double-tangent construction) varies as g(1) infinity L-2d/(d+1). The prefactors in all these relations are derived and it is shown that near the bulk critical point this transition shows a standard scaling behavior and the prefactors can be expressed in terms of known universal constants. Also the rounding of this transition at very large but finite L is considered and it is found that the jump in H at H-1 is rounded over an interval Deltam proportional to L-d<^>2/(d+1). Various simulations are interpreted in the light of these predictions, and the possibility to extract the surface free energy of liquid droplets coexisting in a finite volume with supersaturated gas is critically discussed. (C) 2002 Elsevier Science B.V. All rights reserved.