Equilibrium Cluster Distributions of the Three-dimensional Ising Model in the One Phase Region*

We analyse equilibrium cluster distributions obtained numerically from a ferromagnetic king model (simple cubic lattice, 125000 sites and periodic boundary conditions) along the coexistence line and in the one-phase region below T,. We find evidences that the distribution of sizes and energies scales with temperature and external magnetic field giving Binder’s droplet exponent y z 4/9. The mean number of incident (interior and exterior) bonds on a cluster of size I, s,, seems to behave as I” with x z S/IO when not far away from T,. We conclude that while the classical nucleation theory may provide an approximate description around 0.59T,, 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.