The interplay of diffusion and heterogeneity in nucleation of the networked Ising model

Abstract

Nucleation underlies the dynamics of most first-order phase transitions in natural and man-made systems. However, most of the systems of interest are out of equilibrium. Little is known on the effect of nonequilibrium factors on the dynamics of nucleation. Here, we use the forward flux sampling method to investigate the effect of nonequilibrium diffusion on nucleation in small-world Ising networks, wherein spins can be exchanged between nearest-neighboring nodes. We introduce a parameter α to quantify the difference of nucleation rate with and without diffusion. We find that α shows a nonmonotonic dependence on the rewiring probability p of small-world networks. In particular, for different diffusion probability D, a crossover happens at p ≃ 0.17, below which the nucleation rate decreases as D increases, suggesting that the diffusion is against nucleation; while above which the nucleation rate increases with D, indicating that the diffusion is in favor of nucleation. By identifying the distinct features of nucleating clusters along the pathways for different randomness of networks, we reveal the underlying mechanism of such a nontrivial dependence.