Heterogeneous nucleation on complex networks with mobile impurities

We study the heterogeneous nucleation of Ising model on complex networks under a nonequilibrium situation where the impurities perform degree-biased motion controlled by a parameter α. Through the forward flux sampling and detailed analysis on the nucleating clusters, we find that the nucleation rate shows a nonmonotonic dependence on α for small number of impurities, in which a maximal nucleation rate occurs at $\alpha=0$ corresponding to the degree-uncorrelated random motion. Furthermore, we demonstrate the distinct features of the nucleating clusters along the pathway for different preference of impurities motion, which may be used to understand the resonance-like dependence of nucleation rate on the motion bias of impurities. Our theoretical analysis shows that the nonequilibrium diffusion of impurities can always induce a positive energy flux that can facilitate the barrier-crossing nucleation process. The nonmonotonic feature of the average value of the energy flux with α may be the origin of our simulation results