Nucleation times in the two-dimensional Ising model

We consider the distribution of nucleation times in systems with Brownian type dynamics, as described by classical nucleation theory. This is studied for a prototype system: the two-dimensional Ising model with spin-flip dynamics in an external magnetic field. Direct simulation results for the nucleation times, spanning more than four orders of magnitude, are compared with theoretical predictions. In contrast to usual treatments we determine size-dependent droplet free energies and effective transition rates for growth and shrinkage directly from our simulations. The free energies so determined are well described by the classical Becker-Doring expression, provided one uses an effective surface tension that exceeds the macroscopic surface tension by up to 20%. Within this framework there is good agreement between simulation results and theoretical predictions for the mean nucleation time. In addition we consider the short-time behavior of the nucleation probability after an initial quench into the metastable state. We present theoretical estimates and show that these too agree well with simulation results.