Validity of classical nucleation theory for Ising models.

While the classical nucleation theory (CNT) is widely used to predict the rate of first-order phase transitions, its validity has been questioned due to discrepancies with experiments. We systematically test the individual components of CNT by computer simulations of the Ising models and confirm its fundamental assumptions under a wide range of conditions ( h=0.01-0.13J , T=0.44-0.84Tc in two-dimensions and h=0.30-0.60J , T=0.48-0.62Tc in three dimensions). First, CNT accurately predicts the nucleation rate if the correct droplet free energy is provided. Furthermore, theoretical prediction of droplet free energy matches numerical results very well in the two-dimensional (2D) Ising model, if appropriate correction terms are added. This establishes the 2D Ising model as an important reference point where existing theories can predict nucleation rate accurately with no adjustable parameters.