Monte Carlo study of the evaporation/condensation transition of Ising droplets

Abstract

In recent analytical work, Biskup et al. (Europhys. Lett., 60 (2002) 21) studied the behaviour of d-dimensional finite-volume liquid-vapour systems at a fixed excess δN of particles above the ambient gas density. By identifying a dimensionless parameter Δ(δN) and a universal constant Δc(d), they showed in the limit of large system sizes that for Δ < Δc the excess is absorbed in the background (“evaporated” system), while for Δ > Δc a droplet of the dense phase occurs (“condensed” system). Also the fraction λΔ of excess particles forming the droplet is given explicitly. Furthermore, they argue that the same is true for solid-gas systems. By making use of the well-known equivalence of the lattice-gas picture with the spin-(1/2) Ising model, we performed Monte Carlo simulations of the Ising model with nearest-neighbour couplings on a square lattice with periodic boundary conditions at fixed magnetisation, corresponding to a fixed particles excess. To test the applicability of the analytical results to much smaller, practically accessible system sizes, 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 m0, the susceptibility χ and the Wulff interfacial free energy density τW for the infinite system, we were able to determine λΔ numerically in very good agreement with the theoretical prediction.