Evaporation/Condensation of Ising Droplets

Recently Biskup et al. [Europhys. Lett. 60 (2002) 21] studied the behaviour of d-dimensional finite-volume liquid-vapour systems at a fixed excess $\delta N$ of particles above the ambient gas density. They identify a dimensionless parameter $\Delta (\delta N)$ and a universal constant $\Delta_\mathrm{c}(d)$ and show that for $\Delta < \Delta_c$ a droplet of the dense phase occurs while for $\Delta > \Delta_c$ the excess is absorbed in the background. The fraction $\lambda_\Delta$ 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 $\chi$ and interfacial free energy $\tau_\mathrm{W}$ for the infinite system, we were able to determine $\lambda_\Delta$ in very good agreement with the theoretical prediction.