Abramiuk Angelika, Sznajd-Weron Katarzyna
Department of Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
Department of Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
Entropy (Basel). 2020 Jan 19;22(1):120. doi: 10.3390/e22010120.
We study the -voter model with flexibility, which allows for describing a broad spectrum of independence from zealots, inflexibility, or stubbornness through noisy voters to self-anticonformity. Analyzing the model within the pair approximation allows us to derive the analytical formula for the critical point, below which an ordered (agreement) phase is stable. We determine the role of flexibility, which can be understood as an amount of variability associated with an independent behavior, as well as the role of the average network degree in shaping the character of the phase transition. We check the existence of the scaling relation, which previously was derived for the Sznajd model. We show that the scaling is universal, in a sense that it does not depend neither on the size of the group of influence nor on the average network degree. Analyzing the model in terms of the rescaled parameter, we determine the critical point, the jump of the order parameter, as well as the width of the hysteresis as a function of the average network degree 〈 k 〉 and the size of the group of influence .
我们研究具有灵活性的-voter模型，该模型通过有噪声的选民到自我反从众性，能够描述从狂热者的广泛独立性、不灵活性或固执性。在对近似内分析该模型使我们能够推导出临界点的解析公式，在该临界点以下有序（一致）相是稳定的。我们确定了灵活性的作用，其可被理解为与独立行为相关的变化量，以及平均网络度在塑造相变特征方面的作用。我们检验了先前为Sznajd模型推导的标度关系的存在性。我们表明，这种标度是通用的，从某种意义上说，它既不依赖于影响组的大小，也不依赖于平均网络度。通过根据重新缩放的参数分析该模型，我们确定了临界点、序参量的跃变以及作为平均网络度〈k〉和影响组大小函数的滞后宽度。
