Majority-vote model with degree-weighted influence on complex networks
Minsuk Kim, Soon‐Hyung Yook
Abstract
We study the phase transition of the degree-weighted majority vote (DWMV) model on Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s-R\'enyi networks (ERNs) and scale-free networks (SFNs). In this model, a weight parameter $\ensuremath{\alpha}$ 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 $\ensuremath{\lambda}>5$ belongs to the mean-field Ising universality class, regardless of $\ensuremath{\alpha}$. On SFNs with $3<\ensuremath{\lambda}<5$ the model belongs to the Ising universality class only when $\ensuremath{\alpha}=0$. For $\ensuremath{\alpha}>0$ we find that the critical exponents continuously change as $\ensuremath{\alpha}$ increases from $\ensuremath{\alpha}=0$. However, on SFNs with $\ensuremath{\lambda}<3$ we find that the model undergoes a continuous transition only for $\ensuremath{\alpha}=0$, but the critical exponents significantly deviate from those for the mean-field Ising model. For $\ensuremath{\alpha}>0$ on SFNs with $\ensuremath{\lambda}<3$ the model is always in the disordered phase.