论文标题
多状态嘈杂$ Q $ $ $ $ $ $ $ $ Q $ - 淬火与退火障碍的不连续相变
Discontinuous phase transitions in the multi-state noisy $q$-voter model: quenched vs. annealed disorder
论文作者
论文摘要
我们介绍了嘈杂的$ q $ - 投票模型的广义版，这是最受欢迎的意见动力学模型之一，其中选民可以在$ s \ ge 2 $州之一中。就像原始二进制$ q $ voter模型一样，该模型对应于$ s = 2 $，在每个更新时，随机选择的选民只有在所有$ q $ neighlbors处于同一状态时，随机选择的选民都可以符合其$ q $随机选择的邻居（复制其状态）。此外，选民可以独立采取行动，采取随机选择的状态，该州将障碍引入系统。我们考虑两种类型的疾病：（1）退火，这意味着每个选民都可以独立行动，并以$ p $ $ p $且概率$ 1-p $符合对他人的概述，并且（2）淬火，这意味着所有选民的分数$ p $是永久独立的，其余的是构造主义者。我们通过分析和通过蒙特卡洛模拟在完整图上分析模型。我们表明，对于任何$ q> 1 $的状态数量，$ s> 2 $模型显示不连续的相变，与具有二进制意见的模型相反，在这种模型中，仅观察到不连续的相位转换仅以$>>> 5 $。此外，与$ s = 2 $的情况不同，对于$ s> 2 $不连续的相位过渡在猝灭障碍下幸存下来，尽管它们的锋利程度不如退火。
We introduce a generalized version of the noisy $q$-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $s \ge 2$ states. As in the original binary $q$-voter model, which corresponds to $s=2$, at each update randomly selected voter can conform to its $q$ randomly chosen neighbors (copy their state) only if all $q$ neighbors are in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability $p$ and with complementary probability $1-p$ conform to others, and (2) quenched, which means that there is a fraction $p$ of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states $s>2$ model displays discontinuous phase transitions for any $q>1$, on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $q>5$. Moreover, unlike the case of $s=2$, for $s>2$ discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.
