Simulations of a non-Markovian description of nucleation

Abstract

In most nucleation theories, the state of a nucleating system is described by a distribution of droplet masses and this distribution evolves as a memoryless stochastic process. This is incorrect for a large class of nucleating systems. In a recent paper [ J. Kuipers and G. T. Barkema, Phys. Rev. E 79, 062101 (2009) ], we presented a non-Markovian model for droplet growth that includes memory effects and this model was treated analytically in the absence of a free energy landscape. In this paper, the model is considered with a free energy barrier present. Nucleation rates are measured in the prototypical example of nucleation in the Ising model. Results of direct simulations and the non-Markovian theory agree within a factor of 2 for spin-flip dynamics, and within 20% for local spin-exchange dynamics, even though the measured nucleation rates vary over 27 orders of magnitude