Equilibrium cluster distributions of the three-dimensional Ising model in the one phase region

We analyse equilibrium cluster distributions obtained numerically from a ferromagnetic Ising model (simple cubic lattice, 125000 sites and periodic boundary conditions) along the coexistence line and in the one-phase region below T_c. We find evidences that the distribution of sizes and energies scales
with temperature and external magnetic field giving Binder’s droplet exponent y = 4/9. The mean number of incident (interior and exterior) bonds on a cluster of size l, s_l, seems to behave as l^x with x = 9/10 when not far away from T_c. We conclude that while the classical nucleation theory may provide an approximate description around 0.59T_c, it has to be modified at higher (and lower) temperatures. The Fisher droplet model and the approach by Penrose et al. based on a renormalized fugacity are also discussed. We thus obtain simple semiphenomenological expressions for the cluster equilibrium distributions and partition functions.