Alencar D S M, Alves T F A, Lima F W S, Ferreira R S, Alves G A, Macedo-Filho A
Departamento de Física, Universidade Federal do Piauí, 57072-970 Teresina - PI, Brazil.
Departamento de Ciências Exatas e Aplicadas, Universidade Federal de Ouro Preto, 35931-008 João Monlevade - MG, Brazil.
Phys Rev E. 2023 Jul;108(1-1):014308. doi: 10.1103/PhysRevE.108.014308.
We discuss the majority vote model coupled with scale-free networks and investigate its critical behavior. Previous studies point to a nonuniversal behavior of the majority vote model, where the critical exponents depend on the connectivity. At the same time, the effective dimension D_{eff} is unity for a degree distribution exponent 5/2<γ<7/2. We introduce a finite-size theory of the majority vote model for uncorrelated networks and present generalized scaling relations with good agreement with Monte Carlo simulation results. Our finite-size approach has two sources of size dependence: an external field representing the influence of the mass media on consensus formation and the scale-free network cutoff. The critical exponents are nonuniversal, dependent on the degree distribution exponent, precisely when 5/2<γ<7/2. For γ≥7/2, the model is in the same universality class as the majority vote model on Erdős-Rényi random graphs. However, for γ=7/2, the critical behavior includes additional logarithmic corrections.
我们讨论了与无标度网络相结合的多数投票模型，并研究了其临界行为。先前的研究指出多数投票模型具有非普适行为，其中临界指数取决于连通性。同时，对于度分布指数5/2 < γ < 7/2，有效维度D_{eff}为1。我们引入了针对不相关网络的多数投票模型的有限尺寸理论，并给出了与蒙特卡罗模拟结果吻合良好的广义标度关系。我们的有限尺寸方法有两个尺寸依赖性来源：一个表示大众媒体对共识形成影响的外场，以及无标度网络截止。当5/2 < γ < 7/2时，临界指数是非普适的，取决于度分布指数。对于γ≥7/2，该模型与厄多斯-雷尼随机图上的多数投票模型属于同一普适类。然而，对于γ = 7/2，临界行为包括额外的对数修正。
