819 research outputs found
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
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
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