title: Critical noise of majority-vote model on complex networks.
abstract: The majority-vote model with noise is one of the simplest nonequilibrium statistical model that has been extensively studied in the context of complex networks. However, the relationship between the critical noise where the order-disorder phase transition takes place and the topology of the underlying networks is still lacking. In this paper, we use the heterogeneous mean-field theory to derive the rate equation for governing the model's dynamics that can analytically determine the critical noise f(c) in the limit of infinite network size N→∞. The result shows that f(c) depends on the ratio of 〈k〉 to 〈k(3/2)〉, where 〈k〉 and 〈k(3/2)〉 are the average degree and the 3/2 order moment of degree distribution, respectively. Furthermore, we consider the finite-size effect where the stochastic fluctuation should be involved. To the end, we derive the Langevin equation and obtain the potential of the corresponding Fokker-Planck equation. This allows us to calculate the effective critical noise f(c)(N) at which the susceptibility is maximal in finite-size networks. We find that the f(c)-f(c)(N) decays with N in a power-law way and vanishes for N→∞. All the theoretical results are confirmed by performing the extensive Monte Carlo simulations in random k-regular networks, Erdös-Rényi random networks, and scale-free networks.
authors.affiliation: School of Physics and Material Science, Anhui University, Hefei 230039, China.
authors.forename: Hanshuang
authors.initials: H
authors.lastname: Chen
authors.affiliation: Department of Physics, Anqing Normal University, Anqing 246011, China.
authors.forename: Chuansheng
authors.initials: C
authors.lastname: Shen
authors.affiliation: School of Physics and Material Science, Anhui University, Hefei 230039, China.
authors.forename: Gang
authors.initials: G
authors.lastname: He
authors.affiliation: School of Mathematical Science, Anhui University, Hefei 230039, China.
authors.forename: Haifeng
authors.initials: H
authors.lastname: Zhang
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscales & Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China.
authors.forename: Zhonghuai
authors.initials: Z
authors.lastname: Hou