Evaporation/condensation of Ising droplets - Nuβbaumer, Andreas; Bittner, Elmar; Janke, Wolfhard (Arxiv, 2005)
Recently Biskup et al. [Europhys. Lett. 60 (2002) 21] studied the behaviour of d-dimensional finite-volume liquid-vapour systems at a fixed excess $δ N$ of particles above the ambient gas density. They identify a dimensionless parameter $Δ (δ N)$ and a universal constant $Δ_c(d)$ and show that for $Δ < Δ_c$ a droplet of the dense phase occurs while for $Δ > Δ_c$ the excess is absorbed in the background. The fraction $λ_Δ$ of excess particles forming the droplet is given explicitly. Furthermore, they state, that the same is true for solid-gas systems. To verify these results, we have simulated the spin-1/2 Ising model on a square lattice at constant magnetisation equivalent to a fixed particle excess in the lattice-gas picture. We measured the largest minority droplet, corresponding to the solid phase, at various system sizes ($L=40, ..., 640$). Using analytic values for the spontaneous magnetisation $m_0$, the susceptibility $χ$ and interfacial free energy $τ_W$ for the infinite system, we were able to determine $λ_Δ$ in very good agreement with the theoretical prediction.
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