In this work, we study the opinion dynamics of majority-rule model on a complete graph with additional social behavior namely anticonformity. We consider four spins with three-one interaction; three spins persuade the fourth spin in the population. We perform analytical and numerical calculations to find the critical behavior of the system. From both, we obtained the agreement results, e.g. the system undergoes a second-order phase transition and the critical point of the system only depends on the population number. In addition, the critical point decays exponentially as the number population increases. For the infinite population, the obtained critical point is 1∕6, which agrees well with that of the previous work. We also obtained the critical exponents β≈0.5,γ≈1, and ν≈2 of the model, thus, the model is in the same universality class with the mean-field Ising.

中文翻译：

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基于多数规则模型的三一自旋相互作用的相变和普适性

在这项工作中，我们在一个完整的图上研究了多数规则模型的意见动态，该图具有额外的社会行为，即反整合。我们考虑具有三一相互作用的四次自旋；三个旋转说服了人口中的第四个旋转。我们执行分析和数值计算以找到系统的关键行为。从两者中，我们得到了一致的结果，例如系统经历了二阶相变，系统的临界点仅取决于种群数量。此外，随着人口数量的增加，临界点呈指数衰减。对于无限人口，得到的临界点是1∕6，这与之前的工作非常吻合。我们还获得了临界指数β≈0.5,γ≈1,和ν≈2因此，该模型与平均场 Ising 属于同一普遍性类。