Heterogeneous nucleation on complex networks with mobile impurities

We study the heterogeneous nucleation of Ising model on complex networks under a non-equilibrium situation where the impurities perform degree-biased motion controlled by a parameter \alpha. Through the forward flux sampling and detailed analysis on the nucleating clusters, we find that the nucleation rate shows a nonmonotonic dependence on \alpha 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 \alpha may be the origin of our simulation results.Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:1202.423

Quenched mean-field theory for the majority-vote model on complex networks

The majority-vote (MV) model is one of the simplest nonequilibrium Ising-like model that exhibits a continuous order-disorder phase transition at a critical noise. In this paper, we present a quenched mean-field theory for the dynamics of the MV model on networks. We analytically derive the critical noise on arbitrary quenched unweighted networks, which is determined by the largest eigenvalue of a modified network adjacency matrix. By performing extensive Monte Carlo simulations on synthetic and real networks, we find that the performance of the quenched mean-field theory is superior to a heterogeneous mean-field theory proposed in a previous paper [Chen \emph{et al.}, Phys. Rev. E 91, 022816 (2015)], especially for directed networks.Comment: 6 pages, 3 figures, and 1 tabl