Kim Minsuk, Yook Soon-Hyung
Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
Phys Rev E. 2021 Feb;103(2-1):022302. doi: 10.1103/PhysRevE.103.022302.
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.
我们研究了在厄多斯-雷尼网络（ERNs）和无标度网络（SFNs）上度加权多数投票（DWMV）模型的相变。在该模型中，一个权重参数α调整每个节点对其相邻节点的影响程度。通过蒙特卡罗模拟和有限尺寸标度分析，我们发现，对于度指数λ>5的ERNs和SFNs上的DWMV模型，无论α为何值，都属于平均场伊辛普适类。对于3<λ<5的SFNs，该模型仅在α=0时属于伊辛普适类。对于α>0，我们发现随着α从α=0开始增加，临界指数会持续变化。然而，对于λ<3的SFNs，我们发现该模型仅在α=0时经历连续相变，但临界指数与平均场伊辛模型的临界指数有显著偏差。对于λ<3的SFNs上α>0的情况，该模型始终处于无序相。
