Abramiuk-Szurlej Angelika, Lipiecki Arkadiusz, Pawłowski Jakub, Sznajd-Weron Katarzyna
Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370, Wrocław, Poland.
Sci Rep. 2021 Sep 6;11(1):17719. doi: 10.1038/s41598-021-97155-0.
We study the binary q-voter model with generalized anticonformity on random Erdős-Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence [Formula: see text] in case of conformity is independent from the size of the source of influence [Formula: see text] in case of anticonformity. For [Formula: see text] the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for [Formula: see text], where [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text]. In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree [Formula: see text] observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of [Formula: see text]. Moreover, we show that for [Formula: see text] pair approximation results overlap the Monte Carlo ones. On the other hand, for [Formula: see text] pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to [Formula: see text], as long as the pair approximation indicates correctly the type of the phase transition.
我们研究了在随机厄多斯-雷尼（Erdős-Rényi）图上具有广义反从众性的二元q-投票者模型。在这样一个模型中，两种类型的社会反应，即从众和反从众，以互补概率发生，并且从众情况下影响源的规模[公式：见正文]与反从众情况下影响源的规模[公式：见正文]相互独立。对于[公式：见正文]，该模型简化为具有反从众性的原始q-投票者模型。此前，这样一个广义模型仅在完全图上进行了研究，这对应于平均场方法。结果表明，对于[公式：见正文]，它可以显示不连续相变，其中[公式：见正文]时[公式：见正文]，[公式：见正文]时[公式：见正文]。在本文中，我们提出一个问题：在具有社会网络中经验观察到的平均节点度[公式：见正文]的随机图上，不连续相变是否依然存在。通过使用对近似以及蒙特卡罗模拟，我们表明即使对于相对较小的[公式：见正文]值，不连续相变确实可以存在。此外，我们表明对于[公式：见正文]，对近似结果与蒙特卡罗结果重叠。另一方面，对于[公式：见正文]，对近似给出了定性错误的结果，表明在模拟和平均场方法中均未观察到不连续相变。最后，我们报告了一个有趣的结果，表明只要对近似正确地指出相变类型，在对近似和平均场方法中获得的亚稳极限之间的差异相对于[公式：见正文]遵循幂律。
