Majority-vote model with degree-weighted influence on complex networks.

Abstract

We study the phase transition of the degree-weighted majority vote (DWMV) model on Erdős-Rényi networks (ERNs) and scale-free networks (SFNs). In this model, a weight parameter α adjusts the level of influence of each node on its connected neighbors. Through the Monte Carlo simulations and the finite-size scaling analysis, we find that the DWMV model on ERNs and SFNs with degree exponents λ>5 belongs to the mean-field Ising universality class, regardless of α. On SFNs with 3<λ<5 the model belongs to the Ising universality class only when α=0. For α>0 we find that the critical exponents continuously change as α increases from α=0. However, on SFNs with λ<3 we find that the model undergoes a continuous transition only for α=0, but the critical exponents significantly deviate from those for the mean-field Ising model. For α>0 on SFNs with λ<3 the model is always in the disordered phase.